Understanding the effective stress coefficient for seismic velocity is important for geophysical applications such as overpressure prediction from seismic data as well as for hydrocarbon production and monitoring using time-lapse seismic measurements. This quantity is still not completely understood. Laboratory measurements show that the seismic velocities as a function of effective stress yield effective stress coefficients less than one and usually vary between 0.5 and 1. At the same time, theoretical analysis shows that for an idealized monomineral rock, the effective stress coefficient for elastic moduli (and therefore also for seismic velocities) will always equal one. We explore whether this deviation of the effective stress coefficient from unity can be caused by the spatial microheterogeneity of the rock. The results show that only a small amount (less than 1%) of a very soft component is sufficient to cause this effect. Such soft material may be present in grain contact areas of many rocks and may explain the variation observed experimentally.