Highly active antiretroviral therapy (HAART), administered to a HAART-naïve patient, perturbs the steady state of chronic infection. This perturbation provides an opportunity to investigate the existence and dynamics of different sources of viral production. Models of HIV dynamics can be used to make a comparative analysis of the efficacies of different drug regimens. When HAART is administered for long periods of time, most patients achieve 'undetectable' viral loads (VLs), i.e., below 50 copies/ml. Use of an ultrasensitive VL assay demonstrates that some of these patients obtain a low steady state VL in the range 5-50 copies/ml, while others continue to exhibit VL declines to below 5 copies/ml. Interestingly, when patients exhibit continued declines below 50 copies/ml the virus has a half-life of approximately 6 months, consistent with some estimates of the rate of latent cell decline. Some patients, despite having sustained undetectable VLs, show periods of transient viremia (blips). We present a statistical characterization of the blips observed in a set of 123 patients, suggesting that patients have different tendencies to show blips during the period of VL suppression, that intermittent episodes of viremia have common amplitude profiles, and that VL decay from the peak of a blip may have two phases.