We investigate how costs of choosiness affect the evolution of assortative mating in a simple model of competitive speciation. The model allows for a comprehensive analysis by analytical and numerical techniques. We obtain results for two types of costs: mating costs, which restrict the number of males a choosy female can evaluate, and viability costs, which decrease a choosy female's survival. Mating costs significantly reduce the range of parameters for which speciation is possible, but only if the number of males a female can evaluate is small (less than 10). This type of costs can be eliminated if females are allowed to mate randomly at the end of the mating period. Although, in this case, it is not possible to achieve complete reproductive isolation, our results show partial isolation with strong phenotypic clustering. Viability costs counteract selection for assortative mating. As this selection is typically weak, speciation is possible only if viability costs, too, are weak. The above restrictions are less severe if extreme phenotypes have an intrinsically higher carrying capacity.