Human immunodeficiency virus 1 (HIV) latency remains a significant obstacle to curing infected patients. One promising therapeutic strategy is to purge the latent cellular reservoir by activating latent HIV with latency-reversing agents (LRAs). In some cases, co-drugging with multiple LRAs is necessary to activate latent infections, but few studies have established quantitative criteria for determining when co-drugging is required. Here we systematically quantified drug interactions between histone deacetylase inhibitors and transcriptional activators of HIV and found that the need for co-drugging is determined by the proximity of latent infections to the chromatin-regulated viral gene activation threshold at the viral promoter. Our results suggest two classes of latent viral integrations: those far from the activation threshold that benefit from co-drugging, and those close to the threshold that are efficiently activated by a single drug. Using a primary T cell model of latency, we further demonstrated that the requirement for co-drugging was donor dependent, suggesting that the host may set the level of repression of latent infections. Finally, we showed that single drug or co-drugging doses could be optimized, via repeat stimulations, to minimize unwanted side effects while maintaining robust viral activation. Our results motivate further study of patient-specific latency-reversing strategies.