Despite the success of potent combination therapies in patients with limited or no prior antiretroviral therapy, clinical experience demonstrates that these regimens are less likely to achieve durable suppression of HIV-1 replication in patients with extensive prior treatment with nucleoside analogues. The response to treatment of patients who have failed multiple previous regimens has been disappointing. Thus, there is an urgent need for new approaches to the treatment of such patients. Recent studies have shown that it is effective to add investigational drugs to optimized background drug regimens that have been selected based on resistance testing. This study will assess the virologic and immunologic activity of amdoxovir (DAPD) versus placebo in combination with enfuvirtide (T-20, or ENF) plus optimized background (OB) antiretroviral therapy for highly treatment-experienced patients.