Development of new therapeutics for a rare disease such as cystic fibrosis (CF) is hindered by challenges in accruing enough patients for clinical trials. Using external controls from well-matched historical trials can reduce prospective trial sizes, and this approach has supported regulatory approval of new interventions for other rare diseases. We consider three statistical methods that incorporate external controls into a hypothetical clinical trial of a new treatment to reduce pulmonary exacerbations in CF patients: 1) inverse probability weighting, 2) Bayesian modeling with propensity score-based power priors, and 3) hierarchical Bayesian modeling with commensurate priors. We compare the methods via simulation study and in a real clinical trial data setting. Simulations showed that bias in the treatment effect was <4% using any of the methods, with type 1 error (or in the Bayesian cases, posterior probability of the null hypothesis) usually <5%. Inverse probability weighting was sensitive to similarity in prevalence of the covariates between historical and prospective trial populations. The commensurate prior method performed best with real clinical trial data. Using external controls to reduce trial size in future clinical trials holds promise and can advance the therapeutic pipeline for rare diseases.