For a new, more complex floral form to become established in a population it must overcome the problem of frequency-dependent constancy to successfully attract pollinators. This may be achieved by complex floral forms offering absolute greater rewards than the simpler forms, or by complex flowers offering a higher probability of being rewarding because fewer pollinators are able to visit them. In this paper we examine the effect of three pollinator foraging strategies on the ratio of flights within and between floral morphs and hence on the probability of a new morph establishing in a population without offering a greater reward. We incorporate pollinator behaviour based around observations of two pollinator species systems into three models of competition for pollinators. In the first model the constancy of the pollinator of the new floral morph is a function only of the foraging strategy of the existing pollinator of the original floral morph. In the next model the constancy of the second pollinator is determined by the number of rewarding flowers of each floral morph left by the original pollinator and in the third model it is determined by the ratio of rewarding flowers of each morph left by the original pollinator. The results demonstrate that under conditions of intense competition for pollinators, new, more complex floral forms are indeed able to attract high levels of constant pollinators without offering intrinsically higher rewards. However, for this to occur constancy in one of the pollinators must be a function of the ratio of rewarding to non-rewarding flowers of both floral forms. One prediction from our results is that sympatric speciation of floral complexity based on a higher probability of reward is more likely to occur in flowers offering rewards of pollen rather than nectar. This is because the cost of visiting non-rewarding flowers is usually higher where the reward is pollen rather than nectar. We also predict that complex flowers occurring at low frequency, which offer rewards of nectar, may need intrinsically greater rewards if they are to successfully attract pollinators.