The number of interactions with flower visitor species differs considerably among insect pollinated plants. Knowing the causes for this variation is central to the conservation of single species as well as whole plant–flower visitor communities. Species specific constraints on flower visitor numbers are seldom investigated at the community level. In this study we tested whether flower size parameters set constraints on the morphology of the potential nectar feeding visitors and thus determine the number of visitor species. We studied three possible constraints: the depth and width of tubular structures hiding the nectar (nectar holder depth and width) and the size of flower parts that visitors can land on (size of the alighting place). In addition we assess the role of flower abundance on this relationship. We hypothesized that the stronger size constraints and the smaller flower abundance, the smaller the number of visitor species will be. Our study of a Mediterranean plant–flower visitor community revealed that nectar holder depth, nectar holder width and number of flowers explained 71% of the variation in the number of visitor species. The size of the alighting place did not restrict the body length of the visitors and was not related to visitor species number. In a second step of the analyses we calculated for each plant species the potential number of visitors by determining for each insect species of the local visitor pool whether it passed the morphological limits set by the plant. These potential numbers were highly correlated with the observed numbers (r2=0.5, p<0.001). For each plant species we tested whether the observed visitors were a random selection out of these potential visitors by comparing the mean of the observed and expected proboscis length distributions. For most plant species the observed mean was not significantly different from the random means. Our findings shed light on the way plant–flower visitor networks are structured. Knowing the constraints on interaction patterns will be an important prerequisite to formulate realistic null models and understand patterns of resource partitioning as well as coevolutionary processes.