The purpose of this study is to see whether naltrexone is safe and useful in preventing alcohol relapse, as well as in decreasing craving for alcohol in people with a diagnosis of alcohol and cocaine dependence. Naltrexone is approved by the Food and Drug Administration (FDA) for the treatment of alcohol dependence. However, the medication was not approved as yet at the dosage we will use in this study. The dosage we will use for the study (150 mg), is greater than the recommended dosage from the Physician's Desk Reference (50mg). Unlike other medicines (like Antabuse) useful in the treatment of alcohol dependence, naltrexone will not make you sick if you drink alcohol. Rather, people who are taking this medication have reported that it helps decrease the pleasure associated with drinking for them. This study is being conducted because the medication (Naltrexone) has not been well studied in people with both alcohol and cocaine dependence, so it is still investigational.