Incidence estimation of HIV infection can be performed using recent infection testing algorithm (RITA) results from a cross-sectional sample. This allows practitioners to understand population trends in the HIV epidemic without having to perform longitudinal follow-up on a cohort of individuals. The utility of the approach is limited by its precision, driven by the (low) sensitivity of the RITA at identifying recent infection. By utilizing results of previous HIV tests that individuals may have taken, we consider an enhanced RITA with increased sensitivity (and specificity). We use it to propose an enhanced estimator for incidence estimation. We prove the theoretical properties of the enhanced estimator and illustrate its numerical performance in simulation studies. We apply the estimator to data from a cluster-randomized trial to study the effect of community-level HIV interventions on HIV incidence. We demonstrate that the enhanced estimator provides a more precise estimate of HIV incidence compared to the standard estimator.