In public transit systems with high demand levels, the use of express bus services that serve only a subset of stops along certain routes would seem to be a promising alternative given the benefits they offer to both users and operators. In actual practice, express services in systems such as Transmilenio (Bogota, Colombia), Transantiago (Santiago, Chile), and Metro Rapid (Los Angeles, CA) have proven to be highly appealing. This raises the question about when express services are a reasonable option. Previous work has focused on how some characteristics of the demand structure of a corridor affects the benefits that express services can yield, showing that the load profile shape and the average trip length are crucial. This work presents some evidence that also the dispersion of the demand among different OD pairs (keeping the load profile and the total number of trips constant) affects the potential benefits of express services. As expected the more concentrated the demand into few OD pairs, the more cost savings that can be obtained. To answer this question we developed a methodology to generate OD matrices that share all relevant attributes but differ in variability among OD flows. Thirteen matrices were generated and their optimal sets of bus services with their respective frequencies were obtained. Using the coefficient of variation as a measure of matrix variability, we confirmed that more demand variability (i.e. more flow concentration) gives room to more express services and lower social costs.