Date: 201410
Local time of day: 1201-1800
Location: ZHU.ARTCC, TX
Flight conditions: VMC
Light: Daylight
Aircraft: Embraer Legacy 600 (EMB135BJ)
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZHU
ATC / advisory: Center ZHU
Reporter organization: Air Taxi
Reporter function: First Officer; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Confusion
Second reporter function: Pilot Not Flying; Captain
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Contributing factors: Human Factors; Procedure
Primary problem: Ambiguous

Narrative: While in cruise flight at Flight Level 400 in contact with Houston Center over New Orleans; LA; a descent clearance was issued. The captain; who was the pilot monitoring; read back the clearance and I initiated our descent. Passing Flight Level 388; ATC queried our current altitude and we told him we were descending. He stated that we must have read back a clearance for another aircraft with a similar call sign and we were instructed to climb and maintain Flight Level 400. We immediately complied with the instruction and asked the controller if there were any separation issues. He said we were fine and no further action was needed on our part.


Second narrative: Enroute to DAL on a clearance of direct PNUTS for the MNNDO1 arrival to DAL with Houston Center; approximately 200 miles ESE of PNUTS intersection around New Orleans (I should have got a radial/distance from a VOR but I did not) we were clearly given a descent from FL400 to FL360. I replied with our full call sign and no correction was given. As we were descending 1000 fpm through FL388 Houston Center controller called us and we replied with 'Go ahead'. He replied with 'I think you took someone elses descent; um; go ahead and climb back up to FL400' Which we replied and climbed back to FL400. Shortly after this; he was trying to raise an aircraft multiple times with no answer. We both heard the descent clearance and both know our tail number was used given the descent instruction. There was no traffic on our TCAS; no traffic alert; and no loss of separation. We asked the controller during our hand-off if there is anything we need to follow up on this and he said No; no problem; everything is good.Also on this flight there seemed to be a lot of confusion with our route and ATC. Our initial clearance was Radar Vectors XXX (VOR) XXXXX PNUTS MNNDO1 KDAL. During enroute climb we were given our 2nd clearance Direct REMIS REDFN (not to be confused with REDDN) AEX KDAL. Our 3rd clearance during cruise was Direct PNUTS MNNDO1 KDAL. 25 miles prior to PNUTS the Fort Worth Center controller instructed us to descend via the REDDN1 arrival. I told him we were previously cleared the MNNDO1 and he said 'Really; I'm glad we caught this before you started the arrival; you are now cleared PNUTS REDDN1 to KDAL; descend via the arrival' On the arrival we got put on a heading and then cleared back onto the arrival. On our next frequency change the controller told us to descend via the REEKO1 arrival. I then told him we were on the REDDN1 arrival and he said 'Oh; Ok; descend via the REDDN1 arrival. The REEKO1 arrival doesn't even serve DAL.' There ended up being no problems from our routing; but in the last 15 years of flying this was the most confusion I've seen between controllers on a route/flight plan. I'm not sure if they were having communications problems that day or not; but our next flight was spot on.


Synopsis: Flight crew describes a flight to DAL with four routing and arrival changes after becoming airborne. Enroute at FL400 a descent clearance is issued by ATC and accepted by the crew; but passing FL388 ATC states that the crew must have accepted someone else's clearance and to climb back to FL400.