Two common approaches to regression with missing covariates are complete-case analysis and ignorable likelihood methods. We review these approaches and propose a hybrid class, called subsample ignorable likelihood methods, which applies an ignorable likelihood method to the subsample of observations that are complete on one set of variables, but possibly incomplete on others. Conditions on the missing data mechanism are presented under which subsample ignorable likelihood gives consistent estimates, but both complete-case analysis and ignorable likelihood methods are inconsistent. We motivate and apply the method proposed to data from the National Health and Nutrition Examination Survey, and we illustrate properties of the methods by simulation. Extensions to non-likelihood analyses are also mentioned. © 2011 Royal Statistical Society.