Accurate abundance estimates are critical for informed management of wildlife populations. In New Mexico, USA, minimum counts from aerial surveys are the primary basis for management decisions regarding desert bighorn sheep (Ovis canadensis mexicana); therefore, there is a need to assess methods that account for imperfect detection. Common survey methods for large mammals (i.e., sightability, double-observer, and double-observer sightability models) are known to result in biased estimates, but the presence of radio-collared individuals within a population allows for estimation of residual heterogeneity. Consequently, we explored the use of hybrid double-observer sightability approaches that account for residual heterogeneity when estimating abundance of desert bighorn sheep in the Fra Cristobal Mountains of New Mexico. We collected double-observer sightability data for 167 desert bighorn groups across 3 surveys between December 2016 and November 2017 and compared abundance estimates under 5 modeling methods: a standard sightability model (M_S), a standard double-observer sightability model (M_DS), a hybrid double-observer sightability model incorporating a recapture-type heterogeneity parameter (M_R), a hybrid double-observer sightability model incorporating a mark-type heterogeneity parameter (M_H), and a Lincoln-Petersen estimator. Across all model types, group behavior (moving vs. stationary) and group size influenced detection the most, followed by vegetation class, terrain type, and proportion of obscuring vegetation cover. Standard sightability models produced higher and less precise abundance estimates than all double-observer sightability models. Of the double-observer sightability models, M_R was better supported and estimated greater abundance than M_H and accounted for more bias than M_DS. Both M_R and M_H yielded greater precision than M_S. The M_R models produced an average detection probability of p = 0.72 (SE = 0.02) and abundance estimates of N⌃ = 302 (95% CI = 262−385), N⌃= 290 (95% CI = 261−340), and N⌃= 352 (95% CI = 264−548) for the December 2016, May 2017, and November 2017 surveys, respectively. Lincoln-Petersen estimates of abundance were greater than all double-observer sightability models and similarly precise, but their usefulness is reduced given the requirement to permanently maintain a subset of animals with radio-collars combined with the inability to incorporate information from factors influencing detection probability. Further, because residual heterogeneity models better estimate visibility bias, are flexible in their accommodation of radio-collar data, and can be adapted to unique survey occasions, they present a viable and robust option for estimating desert bighorn sheep abundance.