In genetics, it is often of interest to discover single nucleotide polymorphisms (SNPs) that are directly related to a disease, rather than just being associated with it. Few methods exist, however, for addressing this so-called "true sparsity recovery" issue. In a thorough simulation study, we show that for moderate or low correlation between predictors, lasso-based methods perform well at true sparsity recovery, despite not being specifically designed for this purpose. For large correlations, however, more specialized methods are needed. Stability selection and direct effect testing perform well in all situations, including when the correlation is large.