Marker-trait association analysis is an important statistical tool for detecting DNA variants responsible for genetic traits. In such analyses, an analysis model of the mean genetic effects of the genotypes is often specified. For instance, the effect of the disease allele on the trait is often specified to be dominant, recessive, additive, or multiplicative. Although this model-based approach is powerful when the analysis model is correctly specified, it has been found to have low power sometimes when the specified model is incorrect. We introduce an approach that does not require the specification of a particular genetic model. This approach is built upon a constrained maximum likelihood in which the mean genetic effect of the heterozygous genotype is required to not exceed those of the two homozygous genotypes. The asymptotic distribution of the likelihood-ratio statistic is derived for two special cases. A simulation study suggests that this new approach has power comparable to that of the model-based method when the analysis model is correctly specified. This approach uses one marker at a time (i.e., it is a single-marker analysis). However, given the latest findings that powerful inferential procedures for haplotype analyses can be constructed from single-marker analyses, we expect this approach to be useful for haplotype analyses.