Estimation of an HIV incidence rate based on a cross-sectional sample of individuals evaluated with both a sensitive and less-sensitive diagnostic test offers important advantages to incidence estimation based on a longitudinal cohort study. However, the reliability of the cross-sectional approach has been called into question because of two major concerns. One is the difficulty in obtaining a reliable external approximation for the mean "window period" between detectability of HIV infection with the sensitive and less-sensitive test, which is used in the cross-sectional estimation procedure. The other is how to handle false negative results with the less-sensitive diagnostic test; that is, subjects who may test negative-implying a recent infection-long after they are infected. We propose and investigate an augmented design for cross-sectional incidence estimation studies in which subjects found in the recent infection state are followed for transition to the nonrecent infection state. Inference is based on likelihood methods that account for the length-biased nature of the window periods of subjects found in the recent infection state, and relate the distribution of their forward recurrence times to the population distribution of the window period. The approach performs well in simulation studies and eliminates the need for external approximations of the mean window period and, where applicable, the false negative rate.