Many factors could influence progress towards sympatric speciation. Some of the potentially important ones include competition, mate choice and the degree to which alternative sympatric environments (resources) are discrete. What is not well understood is the relative importance of these different factors, as well as interactions among them. We use an individual-based numerical model to investigate the possibilities. Mate choice was modelled as the degree to which male foraging traits influence female mate choice. Competition was modelled as the degree to which individuals with different phenotypes compete for portions of the resource distribution. Discreteness of the environment was modelled as the degree of bimodality of the underlying resource distribution. We find that strong mate choice was necessary, but not sufficient, to cause sympatric speciation. In addition, sympatric speciation was most likely when the resource distribution was strongly bimodal and when competition among different phenotypes was intermediate. Even under these ideal conditions, however, sympatric speciation occurred only a fraction of the time. Sympatric speciation owing to competition on unimodal resource distributions was also possible, but much less common. In all cases, stochasticity played an important role in determining progress towards sympatric speciation, as evidenced by variation in outcomes among replicate simulations for a given set of parameter values. Overall, we conclude that the nature of competition is much less important for sympatric speciation than is the nature of mate choice and the underlying resource distribution. We argue that an increased understanding of the promoters and inhibitors of sympatric speciation is best achieved through models that simultaneously evaluate multiple potential factors.