Significance In persons living with HIV-1 who start antiretroviral therapy, virus in the blood decreases rapidly to below the detection limit. The decrease occurs in two phases: a rapid initial decrease in the first weeks, followed by a second, slower phase occurring over the next few months. These decay processes are important because infected cells that remain may become part of the stable latent reservoir that prevents cure. The decay in virus levels in blood presumably reflects the loss of infected cells, but the relationship between the decay of free virus and of infected cells has been unclear. Here, we have analyzed this question using an assay that distinguishes between cells with intact and defective forms of the viral genome.