Species distribution models are useful for estimating the distribution and environmental preferences of rare species, but these same species are challenging to model on account of sparse data. We contrast a traditional single-species approach (generalized linear models, GLMs) with two promising frameworks for modeling rare species: ensembles of small models (ESMs), which average across simple models; and multispecies distribution models (MSDMs), which allow rarer species to benefit from statistical 'borrowing of strength' from more common species. Using a virtual species within a community of real species, we evaluated how model accuracy was influenced by the number of occurrences of the rare species (N = 2-64), niche breadth, and similarity to more numerous species' niches. For discriminating between presence and absence, ESMs with just linear terms (ESM-L) performed best for N ≤ 4, whereas for GLMs and ESMs with polynomial terms (ESM-P) were best for N ≥ 8. For calibrating the species' response to influential variables, the MSDM hierarchical modeling of species communities (HMSC) and ESM-P were best for species with niches similar to those of other species. For species with dissimilar niches, ESM-P did best for N ≥ 8, but no model was well calibrated for smaller sample sizes. For identifying uninfluential variables, ESM-L and species archetype models (SAMs), a type of MSDM, did well for ≤ 4, and ESM-L for N ≥ 8. Models of species with narrow niches dissimilar to others had the highest discrimination capacity compared to models for generalist species and/or species with niches similar to other species' niches. 'Borrowing of strength' in MSDMs can assist with some inference tasks, but does not necessarily improve predictions for rare species; simpler, single-species models may be better at a given task. The best algorithm depends on modeling goal (discrimination versus calibration), sample size, and niche breadth and similarity.