The widespread use of generalized linear models in case–control genetic studies has helped to identify many disease-associated risk factors typically defined as DNA variants, or single-nucleotide polymorphisms (SNPs). Up to now, most literature has focused on selecting a unique best subset of SNPs based on some statistical perspective. When the noise is large compared with the signal, however, multiple biological paths are often found to be supported by a given data set. We address the ambiguity related to SNP selection by constructing a list of models—called a variable-selection confidence set (VSCS)—which contains the collection of all well-supported SNP combinations at a user-specified confidence level. The VSCS extends the familiar notion of confidence intervals in the variable-selection setting and provides the practitioner with new tools aiding the variable-selection activity beyond trusting a single model. On the basis of the VSCS, we consider natural graphical and numerical statistics measuring the inclusion importance of an SNP based on its frequency in the most parsimonious VSCS models. This work is motivated by available case–control genetic data on age-related macular degeneration, which is a widespread disease and leading cause of loss of vision. © 2019 Royal Statistical Society