#### UNITED STATES of America, Plaintiff-Appellee, v. Gene Wesley HARTSELL, a/k/a Gene Wesley Gabe Hartsell, Defendant-Appellant. UNITED STATES of America, Plaintiff-Appellee, v. Keith Norland EIDSON, Defendant-Appellant. UNITED STATES of America, Plaintiff-Appellee, v. CHEROKEE RESOURCES, INCORPORATED, Defendant-Appellant.

Nos. 94-5796, 94-5797, 94-5804.

United States Court of Appeals, Fourth Circuit.

Argued Feb. 2, 1996.

Decided Oct. 6, 1997.

*345ARGUED: Dale Stuart Morrison, Law Offices of Dale S. Morrison, Charlotte, NC, for Appellants Eidson and Cherokee Resources; Edward Anthony Fiorella, Jr., Harkey, Lambeth, Nystrom *&*Fiorella, Charlotte, NC, for Appellant Hartsell. Ellen J. Durkee, Environment & Natural Resources Division, United States Department of Justice, Washington, DC, for Appellee. ON BRIEF: Lois J. Sehiffer, Assistant Attorney General, David C. Shilton, Environment & Natural Resources Division, United States Department of Justice, Washington, DC; Mark T. Calloway, United States Attorney, Peter Crane Anderson, Assistant United States Attorney, Charlotte, NC, for Appellee.

Before ERVIN and MOTZ, Circuit Judges, and BLAKE, United States District Judge for the District of Maryland, sitting by designation.

Affirmed by published opinion. Judge ERVIN wrote the opinion, in which Judge MOTZ and Judge BLAKE joined.

OPINION

ERVIN, Circuit Judge:

Appellants, Cherokee Resources, Inc., Keith Norland Eidson and Gene Wesley Hartsell were convicted, following a jury trial, of numerous violations of the Clean Water Act (CWA), 33 U.S.C. § 1311*et seq.*They appeal their convictions and their sentences, raising dozens of challenges to the validity of *346their trials. For the reasons hereinafter explored, we affirm in all respects.

I

Both the factual history and the statutory and regulatory scheme in this case are quite complex, and a brief overview of both is necessary. Cherokee Resources, Inc., (Cherokee) operated a wastewater treatment and oil reclamation business in Charlotte, North Carolina. Eidson was the president of Cherokee and Hartsell was the vice-president and sole shareholder. Both were involved in overseeing Cherokee’s compliance with environmental regulations including the CWA.

In the course of its business, Cherokee accepted oil and industrial wastewater from its customers, processed the oil for re-use and treated the wastewater, and periodically released treated wastewater into the public sewer system. Cherokee’s discharges flowed through the sewer to the Irwin Creek Sewage Treatment Plant. This plant is considered a publicly owned treatment works, “POTW,” in the CWA statutory and regulatory scheme. The plant is operated by the Charlotte-Mecklenburg Utility Department (CMUD). The water treated at Irwin Creek Plant eventually flows into Irwin Creek and then into the Catawba River. The river then continues on into South Carolina, emptying into the Atlantic Ocean in Charleston.

The CWA and its interpretive regulations require POTWs, including Irwin Creek, to issue pretreatment permits to industrial sources specifying levels at which those sources can discharge certain pollutants into the public sewer system. The authority to administer the permit program and issue necessary permits was delegated to North Carolina and its agencies pursuant to the CWA. *See*33 U.S.C. § 1342(c). The program pursuant to which the permits are issued is designed to monitor and limit pollutants in industrial wastewater and is overseen by the Environmental Protection Agency (EPA) and the North Carolina Department of Health, Environment and Natural Resources. Discharge permits issued to industrial dischargers generally last for one to three years.

On May 15, 1990, CMUD issued Cherokee a pretreatment permit limiting the quantities and concentrations of specific pollutants Cherokee could discharge into the sewer. A second permit was issued on June 3, 1991, and a third permit was issued on November 1,1992. North Carolina law allows regulated parties a thirty day period within which to comment about or object to the limits contained in a pretreatment permit. *See*15 N.C.A.C. 2H.0900 (1987). Cherokee never made any response to any of the permits issued to it.

Cherokee’s discharge permits contained several provisions including (1) a general prohibition against “bypassing” water treatment and discharge monitoring facilities; (2) sampling and monitoring requirements to insure Cherokee’s compliance with the permit; and (3) limitations on amounts and concentrations of specific pollutants discharged. Pursuant to the CWA scheme and the permits, Cherokee was required to self-monitor its discharges and it hired outside private laboratories to conduct its self-monitoring. CMUD also conducted routine tests of Cherokee’s discharges.

In the summer of 1990, CMUD tests and Cherokee’s self-monitoring both revealed excessive levels of certain toxic pollutants in Cherokee’s discharges including cadmium, chromium, copper, lead, nickel and zinc. Every time tests were conducted, either by Cherokee’s self-monitoring process or by CMUD with Cherokee’s knowledge, excessive discharges were discovered. As these violations of Cherokee’s permits were discovered, CMUD sent notices of the violations to inform the company that it was discharging in substantial excess of the legal limits imposed by its permits. The violation notices also required Cherokee to do four consecutive days of self-monitoring within thirty days of receipt of the notice, in addition to the occasional self-monitoring already required of all industrial dischargers. However, Cherokee’s discharges of illegal levels of toxic pollutants did not end, despite the repeated notices.

In 1990, CMUD’s Systems “Protection Division Manager and Pretreatment Coordinator,” Robert Griffin, began to suspect that *347Cherokee’s repeated and severe permit violations were the result of illegal or abnormal operations. Griffin notified Federal Bureau of Investigation (FBI) Special Agent Thomas Burleson of his concerns. The FBI began its investigation of Cherokee in early 1991.

In addition to the FBI investigation, CMUD increased its monitoring of Cherokee’s discharges, conducting surreptitious hourly monitoring for several days in the spring of 1991. During these tests CMUD took samples of water upstream of Cherokee’s “tap” or discharge point and downstream of the tap, so that it could be determined precisely what pollutants Cherokee had put in the water. Before this set of tests was conducted, CMUD cleaned out the sewer line with a high pressure water spray to remove debris and buildup and secure an accurate reading. These careful tests showed that Cherokee was repeatedly and substantially violating its permit levels and that it was often doing so during the night.

In the summer of 1991, Agent Burleson compiled the evidence of Cherokee’s violations and submitted an affidavit in support of a request for a search warrant of Cherokee’s plant and offices. Burleson first described the regulatory scheme of the CWA. He then listed the results of the many tests done by CMUD and the results of Cherokee’s self-monitoring in his affidavit.

Burleson next discussed the Resource Conservation and Recovery Act (RCRA), 42 U.S.C. § 6901*et*seg., which regulates disposal, treatment, storage and transportation of hazardous wastes. Burleson described surveillance of a hazardous waste site apparently owned and run by Cherokee; the surveillance suggested that Cherokee, which had not been issued any proper permits by. state or federal agencies, may have been illegally treating, storing and disposing of hazardous wastes.

On the basis of Burleson’s affidavit, a search warrant was issued on July 19, 1991, allowing search of both Cherokee’s main plant and of the suspected hazardous waste disposal site. The search was conducted between July 17 and July 19,1991.

Following the search, CMUD and Cherokee entered into preliminary negotiations regarding a compliance agreement, pursuant to which Cherokee would agree to conform its behavior to its discharge permit and to environmental laws and regulations. However, CMUD’s monitoring revealed continued severe and frequent permit violations by Cherokee. In addition, following the search, several Cherokee employees came forward and began to describe to authorities the illegal discharge practices engaged in by Cherokee.

Ultimately, the evidence gathered by the investigation of Cherokee and the testimony of the Cherokee employees revealed that the company used several illegal disposal methods, known as “bypass methods” because such practices bypass treatment and monitoring devices and clandestinely discharge pollutants directly into the sewer line. Employees revealed that illegal dumping occurred because Cherokee accepted far more wastewater and waste oil than it could handle and therefore it often dumped completely untreated water and oil into the sewer system. In one bypass method, Hartsell and Eidson directed employees to pump waste-water through the employees’ toilet. Another illegal technique used by Cherokee was to pump untreated water into a storage tank which had a special valve for rapid discharge and then discharge those pollutants directly into the sewer.

Hartsell, Eidson and Cherokee were charged, in a multi-count indictment, with conspiracy to knowingly violate the CWA, knowingly violating pretreatment standards, and tampering with a pollutant monitoring device. The defendants were tried in April 1994, but that resulted in a mistrial because the jury could not reach a verdict. Following a second trial in June 1994, Hartsell, Eidson and Cherokee were each convicted of conspiracy and of several substantive counts of knowingly violating pretreatment standards, and Eidson and Cherokee were also convicted of tampering with a monitoring device. The court imposed a $50,000 fine on Cherokee, along with a $1400 special assessment, four years’ supervised probation and prosecution costs. Eidson and Hartsell were each sentenced to 51 months and ordered to *348pay individual fines and special assessments. This appeal followed.

II

On appeal, Cherokee, Hartsell and Eidson make almost fifty separate assignments of error. New of these arguments are explained or substantiated, and none persuades us that a reversal of the appellants’ convictions or sentences is required. In this opinion, we will specifically address those of Hartsell’s and Eidson’s countless arguments which are more clearly set forth and comprehensible.

As an initial matter we must turn our attention to the appellants’ assertion that the district court lacked subject matter jurisdiction in the instant case. Although the argument on this matter is not clearly articulated, it appears that Hartsell, Eidson and Cherokee argue that the CWA extends only to “navigable waters.” The appellants argue that their discharges into the public sewer system were not into a navigable waterway and, therefore, the federal government lacks the power to punish such pollution and the federal courts lack the power to hear a case involving such pollution. The appellants also seem to argue that, even if Congress did intend for the CWA to extend to waterways such as the sewer system in the instant case, Congress lacked the constitutional power to regulate such waterways.

We find this argument to be without merit for several reasons. First, the CWA clearly provides for regulation of discharges into public sewer systems such as the Irwin Creek system in the instant case. *See*33 U.S.C. § 1317. The plain language of the CWA prohibits discharge of pollutants into “navigable waters,” except in accordance with a permit issued pursuant to the Act. 33 U.S.C. § 1342. The Act defines navigable waters as “waters of the United States,” 33 U.S.C. § 1362(7), and this broad definition “makes it clear that the term ‘navigable’ as used in the Act is of limited import.” *United States v. Riverside Bayview Homes, Inc.,*474 U.S. 121, 133, 106 S.Ct. 455, 462, 88 L.Ed.2d 419 (1985).

Several courts, including the Supreme Court and this court, have held that Congress clearly intended to regulate pollutant discharge into sewer systems and other non-navigable waters through the CWA, and that Congress has the constitutional authority to do so. In *Riverside Bayview Homes,*the Court stated that Congress intended to allow “broad federal authority to control pollution, for ‘[wjater moves in hydrological cycles and it is essential that discharge of pollutants be controlled at its source.’ ” *Id.*(quoting the Act’s legislative history, S.Rep. No. 92-414, p. 77 (1972)). The Court further held that “Congress clearly intended to *exercise its powers under the Commerce Clause*to regulate at least some waters that would not be deemed ‘navigable’ under the classical understanding of that term.” *Id.*(emphasis added). *See also United States v. Tull,*769 F.2d 182, 184 (4th Cir.1985) (recognizing the broad reach over waterways which Congress intended to give the CWA), *rev’d on other grounds,*481 U.S. 412, 107 S.Ct. 1831, 95 L.Ed.2d 365 (1987); *Hodel v. Virginia Surface Mining & Reclamation Ass’n,*452 U.S. 264, 282, 101 S.Ct. 2352, 2363, 69 L.Ed.2d 1 (1981) (“[W]e agree with the lower federal courts that have uniformly found the power conferred by the Commerce Clause broad enough to permit cpngressional regulation of activities causing air or water pollution, or other environmental hazards that may have effects in more than one State.”); *United States v. Ashland Oil and Transportation Co.,*504 F.2d 1317, 1325 (6th Cir.1974) (holding that pollution of non-navigable waterways can be properly regulated by Congress under the Commerce Clause).1

*349We hold that Congress not only intended to legislate against unchecked discharge of pollutants into public sewers which would eventually flow into streams and rivers, but that Congress acted squarely within its power in so doing. Cherokee, Hartsell and Eidson are unable to persuade us that either Congress, in passing the CWA, or the district court, in hearing the criminal case against the appellants, acted beyond its powers.

Ill

Hartsell, Eidson and Cherokee assert that they were deprived of due process of law when the district court “routinely denied them funds to present their case.” Appellants’ Brief at 22. Hartsell and Eidson were indigent and were therefore entitled to court-appointed representation and to some public funds with which to secure resources necessary to the preparation and presentation of a defense. Hartsell and Eidson assert that the district court unfairly limited the amount of money available to them to pay for defense investigators and experts. Hartsell, Eidson and Cherokee also claim that the district court erred when it declined to appoint counsel to represent Cherokee, a corporation. We hold that these claims are without merit, as the district court provided the appellants with the public resources required by due process considerations.

A

Indigent defendants are entitled by law to money for investigative and expert services that are “necessary for adequate representation.” 18 U.S.C. § 3006A(e)(l). We review a district court’s decision that certain resources are or are not “necessary” for an abuse of discretion. *See Williams v. Martin,*618 F.2d 1021, 1026 (4th Cir.1980); *United States v. Morrison,*946 F.2d 484, 490 (7th Cir.1991), *cert. denied,*506 U.S. 1039, 113 S.Ct. 826, 121 L.Ed.2d 696 (1992). The Supreme Court has made clear that a defendant does not have the right to public funding for all possibly helpful avenues of investigation or all possibly useful expert services, but only to the level of support required by the Due Process Clause. *Ross v. Moffitt,*417 U.S. 600, 616, 94 S.Ct. 2437, 2446, 41 L.Ed.2d 341 (1974). The Court delineated the scope of an indigent defendant’s due process right to public funds to help present a defense, stating that the government has no duty to “duplicate the legal arsenal that may be privately retained ... [but must] assure the indigent defendant an adequate opportunity to present his claims fairly.” *Id.*Stated differently, a defendant who alleges that a denial of funds has violated due process must demonstrate by clear and convincing evidence that the denial resulted in actual prejudice to the defense. *See United States v. Minor,*756 F.2d 731, 737 (9th Cir.), *cert. granted, judgment vacated by*474 U.S. 991, 106 S.Ct. 401, 88 L.Ed.2d 353 (1985), *on remand to*783 F.2d 154 (9th Cir.1986).

In the instant case Eidson and Hart-sell do not come close to satisfying their burden of proof. The record shows that Hartsell and Eidson were provided with funds for fifty hours of investigative services and fifty hours of expert services, exclusive of testimony in court, to prepare for the first trial. They were then awarded an additional five hours of investigative services and ten hours of expert services between the two trials. Hartsell and Eidson seem to argue that they should have received additional funds before the second trial, to investigate possible new leads and theories of defense. However, the trial strategy used by the government did not change between trials and the evidence presented against the defendants was largely the same. Hartsell and Eidson fail to explain how the outcome of their second trial might have been different had they been provided with more resources for their defense. We conclude, therefore, that Hartsell and Eidson were given the resources necessary to the preparation of a defense as required by considerations of due process.

B

With respect to Cherokee’s claim that the court erred when it declined to appoint *350counsel for the corporation, Cherokee argues that the Criminal Justice Act, (CJA), codified at 18 U.S.C. § 3006A, mandates that counsel be provided to a corporation that cannot afford to secure counsel for itself when it faces criminal charges. However, Cherokee fails to point to the decision of even one court which has held that a company was entitled to appointed counsel and Cherokee cites no language from the CJA which supports its claim.

We find Cherokee’s argument to be unpersuasive. The Ninth Circuit recently held that neither the Sixth Amendment to the United States Constitution nor the Criminal Justice Act provides that counsel must be appointed, at public expense, to represent a corporation in criminal proceedings. *See United States v. Unimex, Inc.,*991 F.2d 546, 550 (9th Cir.1993); *see also United States v. Hoskins,*639 F.Supp. 512, 514 (W.D.N.Y. 1986), *aff'd*875 F.2d 308 (2d Cir.1989). We agree, finding no suggestion anywhere in 18 U.S.C. § 3006A that corporations are entitled to publicly appointed counsel. Moreover, Cherokee does absolutely nothing to show that, even if it were a “person” entitled to representation as provided by the Criminal Justice Act, it would qualify as “a person financially unable to obtain adequate representation....” 18 U.S.C. § 3006A(a). Cherokee does not show that it lacked the funds to secure its own counsel. We conclude that Hartsell, Eidson and Cherokee failed to show that the district court abused its discretion when it limited their access to the federal coffers, either when it limited Hartsell and Eidson’s access to investigative and expert services or when it declined to provide publicly paid representation to Cherokee.

IV

Eidson, Hartsell and Cherokee next assert that they were prosecuted for violating unfair and unclear laws and regulations. As with the other arguments, the appellants’ specific position with respect to this issue is very murky. The appellants seem to argue that the CWA and its interpretative regulations are unconstitutionally vague and that the discharge permits issued to Cherokee were too stringent. For several reasons, we conclude that both of these claims are without merit.

A

We turn first to the vagueness argument. Hartsell, Eidson and Cherokee do not explain their contentions on this issue, but simply state in three *very*eonclusory sentences, that the “laws and regulations used to convict these Defendants were unconstitutionally vague,” and that laws must be sufficiently specific to inform people of what is forbidden. This bald and empty argument is simply inadequate to sustain the appellants’ burden of proving that the CWA is invalid.

The CWA plainly and explicitly provides for the promulgation of regulations which will limit or prohibit the discharge of pollutants into POTWs. 33 U.S.C. § 1317. Those regulations, in turn, mandate the issuance of permits to “Industrial User(s)” which contain specific effluent limits for those users, 40 C.F.R. 403.5(c). The individualized limits in these permits are deemed “standards” within the meaning of 33 U.S.C. § 1317(d), which prohibits the operation of a source of pollutants in violation of pretreatment standards. 40 C.F.R. 403.5(d). Finally, the CWA makes plain that criminal penalties, including imprisonment, will be assessed against those who knowingly violate a “permit condition or limitation” of the statutory and regulatory scheme of the CWA. 33 U.S.C. § 1319(c)(2)(A).

In the instant ease, Cherokee was issued three very specific permits which explicitly informed the company and its officers of the limits on the quantities and concentrations of certain pollutants that could be released into the public sewer system. The combination of laws, regulations, permits and warning letters in this case put Cherokee, Hartsell, and Eidson on *very*clear notice of the conduct which would result in violation of federal law and possible incarceration and fines. A statute is not unconstitutionally vague if it “define[s] the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” *Kolender v. Lawson,*461 U.S. 352, 357, 103 S.Ct. 1855, *3511858, 75 L.Ed.2d 903 (1983); *see also United States v. Weitzenhoff,*35 F.3d 1275, 1289 (9th Cir.1993) (holding, in a case similar to the instant one, that discharge permits provided ample notice that certain behavior on the part of the defendants would violate the law). In the instant case, there is no merit to the appellants’ empty contention that they lacked the constitutionally required notice of the illegal nature of certain acts.2

B

Cherokee, Hartsell and Eidson also argue that the specific permits which were issued to them were unnecessarily strict and arbitrary. They argue that the permits limited their discharge of certain pollutants to a level that was even less than the permissible concentration of those pollutants in ordinary drinking water. Again, we are not persuaded by their analysis.

First, as mentioned above, the North Carolina law which governs the issuánce of permits such as the ones issued to Cherokee specifies that any challenges to discharge limitations set forth in those permits must be raised within 30 days of receipt of the permit. 15 N.C.A.C. 2H.0900 (1987). “Unless such demand is made, the decision on the application shall be final and binding.” *Id.*In this case, Cherokee and its officers never challenged the discharge limits contained in any of the permits issued. Therefore they may not contest those limits before us in their appeal. *See Myers v. Bethlehem Shipbuilding Corp.,*303 U.S. 41, 50-51, 58 S.Ct. 459, 463, 82 L.Ed. 638 (1938) (noting “the long settled rule of judicial administration that no one is entitled to judicial relief for a supposed or threatened injury until the prescribed administrative remedy has been exhausted”); *see also St. Francis Hosp. v. Bowen,*802 F.2d 697, 701 (4th Cir.1986).

Second, the permit program administered by CMUD and the specific permits issued to Cherokee were both developed in compliance with the CWA and its regulations. Among other things CMUD considered the capacity of the Irwin Creek treatment facility, the number of industrial dischargers which discharge into that section of the sewer system and the amounts of their discharge, and federal and state standards for water quality when it issued Cherokee’s permits. Cherokee offers almost no analysis and no legal precedent to support its claim that the permits issued to limit its discharges were too stringent.

Cherokee’s sole support for its claim that its permit levels were too severe is that, for two pollutants, Cherokee was limited to a discharge level that was lower than the drinking water standards for that pollutant. However, as the district court below correctly realized, the regulatory program for discharge into sewers, treatment facilities and, eventually, creeks and rivers created by the pollutant discharge provisions of the CWA serves a different purpose and uses different means than the drinking water standards. For instance, the regulated pollutants could harm waterways and aquatic life, and could introduce chemicals which hamper treatment facilities’ ability to treat waste water, even at levels where they might not directly harm *352humans. Hartsell, Eidson and Cherokee have not shown that it is in any way illegitimate for federal and state agencies to apply stringent standards for certain industrial discharges into sewer systems.3 Moreover, as the government points out, Cherokee’s discharges were so contaminated that they routinely exceeded drinking water standards as well as the limits included in their permits.

V

Hartsell, Eidson and Cherokee argue that the search of the Cherokee facilities and offices was conducted pursuant to an invalid search warrant and therefore the district court erred when it declined to suppress the evidence acquired during that search. This argument is no more clearly articulated than the appellants’ other contentions. In fact Hartsell, Eidson and Cherokee neglect to even mention in their briefs what evidence was seized that they are seeking to suppress. Nonetheless, we are able to glean enough information from the briefs and the record before us to conclude with certainty that the government’s search of Cherokee was legal.

It seems that the appellants’ argument regarding the invalidity of the search warrant has several components. They assert that the affidavit of Agent Burleson, given to the magistrate judge when the search warrant was sought, relied upon discharge tests which were two months old at the time of the warrant; that some of the tests relied upon were not “flow proportioned” and therefore did not test representative samples; and that many of the facts relied upon in the affidavit in support of the warrant dealt with violations of the Resource Conservation and Recovery Act (RCRA) rather than the CWA. However, Hartsell, Eidson and Cherokee fail to show how these facts serve to undercut the magistrate judge’s finding of probable cause.

We find that some of Cherokee’s assertions are simply inaccurate and that others, even if true, do not support its contention that probable cause was lacking. We recognize that a magistrate judge’s determination of probable cause based upon the assessment of facts presented in support of a search warrant is paid “great deference” and overturned only for abuse of discretion. *See United States v. Leon,*468 U.S. 897, 914, 104 S.Ct. 3405, 3416, 82 L.Ed.2d 677 (1984); *United States v. Blackwood,*913 F.2d 139, 142 (4th Cir.1990). We also note that we must review the “totality of the circumstances” presented to the magistrate judge when reviewing whether the warrant was supported by probable cause. *See Illinois v. Gates,*462 U.S. 213, 238, 103 S.Ct. 2317, 2332, 76 L.Ed.2d 527 (1983); *United States v. Lalor,*996 F.2d 1578, 1580 (4th Cir.1993).

When we look at all of the facts presented to the magistrate judge by Burleson in this case, it is clear that there was probable cause to believe that Cherokee and its officers were engaged in illegal activity. Burleson’s affidavit showed that, during every routinely scheduled “sampling event” which tested Cherokee’s discharge, Cherokee exceeded its permit limits for certain pollutants. Further on two different “surreptitious” sampling oe-' casions, in late April and early May of 1991, it was found that Cherokee’s discharges were highly contaminated.4 A single sample was taken on July 1, 1991, two weeks before Burleson sought the warrant, to “freshen” probable cause; that sample as well showed numerous violations of Cherokee’s discharge permit.

These numerous tests measuring discharge of pollutants into the sewer, some of them conducted by Cherokee itself as part of its “self monitoring,” provide more than ample probable cause to believe that Cherokee might be violating the law. While it is true *353that the tests done were not “flow-proportional,” Cherokee does not explain how this rendered the results of those tests completely invalid. As the government points out, “time proportional” tests were used because Cherokee had not installed the equipment necessary to conduct flow proportional tests; the time proportional tests still constituted representative sampling.

Finally, it is true that the affidavit included extensive discussion of evidence which suggested that Cherokee might be flagrantly violating RCRA as well as the CWA. Cherokee, Hartsell and Eidson imply that, because the government eventually decided not to pursue criminal charges under RCRA, the search warrant is invalid because it relied on the RCRA evidence as well as the CWA evidence. However, they offer absolutely no support for this contention. In fact, we find that the portions of the affidavit dealing with the CWA alone were more than enough to provide probable cause to search. Further, the facts related to RCRA were validly considered by the magistrate judge, as they also provided probable cause that laws were being broken, irrespective of the fact that ultimately no charges were brought relating to those facts.

In sum, we hold that the magistrate judge acted well within his discretion when he issued a warrant allowing the government to search Cherokee facilities and offices. Further, even had the warrant been issued in error, Cherokee, Hartsell and.Eidson fail to suggest what evidence should have been suppressed and how exclusion of that evidence would have altered the outcome of their trial. Therefore, they would not be entitled to relief even if they had convinced us that the warrant was invalid.5

VI

Hartsell, Eidson and Cherokee raise two challenges to the indictment. First, they contend that the indictment contains unnecessary and prejudicial surplusage which should have been removed by the district court prior to trial. Second, they assert that counts two through six of the indictment, charging the defendants with discharging contaminants in excess of their permit limits, should have been stricken from the indictment and should never have reached the jury. As with appellants’ other arguments, neither of these claims is clearly articulated, and neither is persuasive.

A

With respect to the “surplusage” in the indictment, Hartsell, Eidson and Cherokee argue that the paragraphs at the beginning of the indictment which explain the CWA and its complex regulatory scheme should have been removed before the jury saw the indictment at trial as those paragraphs were “self-serving and highly prejudicial.” However they do not explain, beyond this single sentence, why these paragraphs even constitute surplusage and how they might have caused any prejudice whatsoever to the defendants. Instead we are persuaded by the government’s assertion that these paragraphs are useful and accurate descriptions of the complex legal scheme. Further, even if the paragraphs were unnecessary, because the district court’s instruction to the jury regarding the relevant law provided the same analysis, we find no indication whatsoever that they were prejudicial. Given that we review the district court’s decision concerning whether or not to strike alleged surplusage from the indictment to see if that decision constitutes an abuse of discretion, *United States v. Poore,*594 F.2d 39, 41 (4th Cir.1979), 1 Wright, *Federal Practice and Procedure,*§ 127 at 426, we find no abuse of discretion in this ease.

*354B

Similarly, we find there to be no merit in appellants’ claim that counts two through six should not have been presented to the jury. It appears that the crux of the argument on this point is that there was insufficient evidence to support a conviction on these counts. Hartsell, Eidson and Cherokee assert that various flaws in the testing methods used to monitor Cherokee’s pollutant discharges rendered those tests inadmissable, or at least not probative of guilt.

When addressing a claim of insufficiency of the evidence, we must affirm a criminal conviction if, in light of the totality of the evidence presented at trial, a rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt. *See United States v. Burgos,*94 F.3d 849, 862-63 (4th Cir.1996) (en banc) (“Critical to our review of sufficiency challenges is the complete picture that the evidence presents.”); *see also Jackson v. Virginia,*443 U.S. 307, 319, 99 S.Ct. 2781, 2788, 61 L.Ed.2d 560 (1979) (“[T]he relevant question is whether, after viewing the evidence in the light most favorable to the prosecution, *any*rational trier of fact could have found the elements of the crime beyond a reasonable doubt.”). In the instant case, the government relied on the results of several different discharge tests and the testimony of former Cherokee employees in convicting Cherokee, Hartsell and Eidson of the illegal discharges in counts two through six. Some of these tests were conducted by Cherokee itself as part of its self-monitoring. Even if the appellants’ claim that the tests conducted and discussed at trial were not perfectly accurate is true, they are unable to show that no reasonable trier of fact, considering the substantial evidence presented in this case, could vote to convict.

VII

In addition to the above-discussed claims, Cherokee, Eidson and Hartsell raise countless additional challenges to their convictions and sentences. For example, they claim that several dozen of the evidentiary decisions made by the district court during trial were erroneous; most of these arguments are each raised in one sentence or less. Hartsell, Eidson and Cherokee also challenge the government’s use of informants, the court’s instructions to the jury, the court’s decision to allow examination of witnesses on certain points and to forbid questioning regarding other matters, and the calculation of their sentences, among other things.

We have closely examined each of these contentions, even though many were scarcely articulated by the appellants themselves. We find that none of these arguments, and none of the more closely addressed contentions explored above, is persuasive. Therefore the convictions and sentences of Cherokee, Hartsell and Eidson are affirmed in their entirety.

*AFFIRMED.*

1

. Hartsell, Eidson and Cherokee argue that the Court’s recent decision in *United States v. Lopez,*514 U.S. 549, 559-61, 115 S.Ct. 1624, 1630, 131 L.Ed.2d 626 (1995), signals a change in Commerce Clause jurisprudence such that the CWA must now be read as an unconstitutional action by Congress. We do not agree that *Lopez*is a radical sea change which invalidates the decades of Commerce Clause analysis, pursuant to which the CWA is certainly a valid exercise of Congressional power. *See United States v. Eidson,*108 F.3d 1336, 1341 (11th Cir.1997) (finding, after *Lopez,*that Congress intended the CWA to have the broadest possible constitutional reach and finding that the Act therefore reaches non-navigable waters). Appellants’ conclusory state*349ments of Commerce Clause philosophy do not persuade us that *Lopez*renders the CWA unconstitutional.

2

. Hartsell, Eidson and Cherokee argue, in a entirely separate section of their brief, that their prosecution violates the prohibition in the United States Constitution against *ex post facto*prosecutions, Article I, Sec. 9. The appellants argue that "[t]he Defendants’ convictions for discharging in excess of a municipal permit were an unforeseeable judicial enlargement of maritime shipping laws and criminal statutes and regulations without the Defendants being given a fair warning their conduct would give rise to criminal penalties.” App. Br. at 28. It is unclear how the appellants’ *ex post facto*argument, as articulated, is distinct from their argument regarding vagueness, but it is clear that the appellants do not understand the nature of the protections afforded by the *ex post facto*clause.

We hold that the *ex post facto*clause was not violated by the government's actions in the instant case as Eidson, Hartsell and Cherokee were prosecuted pursuant to laws and regulations that were clearly "on the books” at the time of the appellants' illegal conduct, and they were given punishments which were already clearly provided for in the law. We note that appellants' reliance on *Marks v. United States,*430 U.S. 188, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977), is misplaced as that case dealt with application of new standards defining illegal hard core pornography to conduct which occurred before those standards were created. That case is plainly inapposite to the instant facts.

3

. Eidson, Hartsell and Cherokee argue, in a separate portion of their briefs, that the district court erred when it precluded them from introducing evidence of drinking water standards at trial so that they could argue that their permits were excessively stringent. However, as explored here, such evidence was properly excluded as it is irrelevant to any issue properly before the judge or jury at trial.

4

. We cannot review the specific quantitative statistics offered by Burleson in support of his affidavit because the attachments, which included graphs showing the extent of Cherokee’s illegal discharges, were omitted from the record before us on appeal.

5

. In a related argument, Hartsell, Eidson and Cherokee assert that the district court should have ordered a *Franks*hearing wherein they could examine Burleson about the "erroneous information” allegedly included in his affidavit to the court when he sought the search warrant. *See Franks v. Delaware,*438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978). We have held that a defendant must first make a showing that an affiant's statement in a warrant affidavit was deliberately or recklessly false *and*that the remaining facts contained in the affidavit are inadequate to sustain a finding of probable cause. *See United States v. Jeffus,*22 F.3d 554, 559 (4th Cir.1994). Hartsell, Eidson and Cherokee made neither showing in the instant case, and the district court correctly denied their request for a hearing.