Part 2: After the highest tolerated dose is established in Part 1, additional patients are randomized to receive HAART alone (Arm 1), HAART with high-dose IL-2 (Arm 2), or HAART with low-dose IL-2 (Arm 3). High-dose IL-2 is given twice daily at the highest dose tolerated in Part 1 for 5 days every 8 weeks for 6 cycles. Low-dose IL-2 is given once a day every day for 48 weeks. For Arms 2 and 3 [AS PER AMENDMENT 5/3/01: (except patients in the pharmacokinetic substudy), it is strongly recommended, but not required, that] IL-2 is given the first week on an inpatient basis by hospital personnel. As in Part 1, there is the option of administering the remaining injections at home. Intensive toxicity monitoring, routine lymphocyte subsets, and quantitative HIV RNA are performed on all patients at specified time points during the study. The first 12 patients in Arms 2 and 3 have pharmacokinetic testing with frequent blood samples drawn at intervals, some of which require staying up to 12 hours at the clinic. Diphtheria/tetanus immunizations and bacteriophage phi X174 immunizations are administered to all patients to determine antibody responses.