Meta-analysis of population-based genetic association studies is often challenged by obstacles associated with the underlying inheritance model. For a simple genetic variant with two alleles, a recessive, dominant or co-dominant model is typically assumed. In the absence of a strong biological rationale for a particular inheritance model, a recently suggested inheritance-model-free approach can be implemented. To enable a flexible choice among these models, summary results from each of the three genotypes are required. Incompatibility of the data across studies because of different inheritance models is a common problem. For instance, if the underlying model is dominant, studies that have assumed the recessive model and presented the results accordingly, have so far been excluded from the meta-analysis. We show how to combine data and make inferences under any inheritance model, irrespective of the models assumed within each study and the way that data are presented. Within a Bayesian framework we describe prospective models for binary and continuous outcomes, and retrospective models for binary outcomes. The methods exploit an assumption of Hardy-Weinberg equilibrium, prior information about genotype prevalence or assumption of a specific inheritance model. On application to meta-analyses of the associations between a polymorphism in the lipoprotein lipase gene and coronary heart disease or high-density lipoprotein cholesterol, we observe substantial gains in precision when there is a large proportion of studies in which different inheritance models have been assumed.