Inclusion Criteria:  Male or female, Veterans and non-Veterans, ages 21 to 50; Able to read and write in English and sign the informed consent; Willing to comply with all study procedures and be available for the duration of the study; ECG that demonstrates no clinically significant conduction issues or arrhythmias; Have no clinically significant contraindications, in the judgement of the PI/study physician, for study participation (based on self-reported medical history and brief physical examination); Have a current diagnosis of Alcohol use disorder (AUD) (mild, moderate, or severe) as determined by MINI-5 and PTSD as determined by the Clinician-Administered PTSD Scale for DSM-5 (CAPS-5); PCL-5 score >33; Must have > 1 heavy drinking episodes (>4 standard drink units (SDU) for men; >3 SDU for women) in the last 30 days (assessed by the Timeline Follow Back (TLFB)). Not be treatment seeking for AUD Females of childbearing potential (not surgically sterilized (tubal ligation/hysterectomy) or not post-menopausal (no menstrual period for > 6 months) must be willing to use a medically acceptable and effective birth control method for 3 months before the study and while participating in the study. Medically acceptable methods of contraception that may be used by the participant include abstinence, birth control pills or patches, birth control implants, diaphragm, intrauterine device (IUD), or condoms.  Exclusion Criteria:  Current bipolar disorder or psychotic disorders as determined by MINI-5; Current diagnosis of a substance use disorder (other than alcohol, nicotine, or marijuana) as determined by MINI-5; Females who are pregnant, nursing, or planning to become pregnant during study participation; Current physiological alcohol dependence requiring a higher level of care (e.g. detox) as determined by study physician conducting physical examination and CIWA score. Tolerance to alcohol will be allowed. Recent history of complicated alcohol withdrawal, alcohol withdrawal seizures, or delirium tremens (DTs); Score > 4 on Clinical Institute Withdrawal Assessment for Alcohol Scale (CIWA-Ar) at randomization; History of major medical illnesses including liver disease, heart disease, chronic pain or other medical conditions that the physician investigator deems contraindicated for the participant to be in the study; Clinically significant history of cardiac disease including (a) chronic hypertension (even if adequately controlled by antihypertensive medications); (b) history of syncope or other syncopal attacks; (c) current evidence of orthostatic hypotension (defined as a decrease in systolic BP of 20 mm Hg or decrease in diastolic BP of 10mm Hg within 3 minutes); (d) resting heart rate of <60 beats per minute; (e) systolic blood pressure <110mmHg or diastolic BP <70mmHg; or (f) participants with a QTC interval >440msec (males) or >46msec (females). Clinically significant medical conditions including hepatic ascites (bilirubin >10% above the upper limit of normal [ULN] or liver function tests [LFT] >3 × ULN); Renal impairment as measured by BUN/Creatinine; Currently taking the following medications: a) medications for alcoholism (e.g. naltrexone, disulfiram, topiramate, acamprosate); b) psychotropic medications that promote sedation including sedative/hypnotics, barbiturates, antihistamines, sedative antidepressants (e.g. doxepin, mirtazapine, trazodone), and triptans (e.g., sumatriptan); c) antihypertensive medications; d) alpha-2-adrenergic agonists (clonidine, guanfacine, lofexidine); or adrenergic agents prescribed for other reasons are excluded (prazosin). (Permitted Concomitant Medications: The concomitant medications allowed in the study include non-sedative antidepressants used to treat PTSD); History of allergic reactions to dexmedetomidine or known allergy to dexmedetomidine; Participation in a clinical trial of a pharmacological agent within 30 days prior to screening; Any finding that, in the view of the principal investigator, would compromise the subject's ability to fulfill the study visit schedule or requirements