We report on a novel speckle reduction scheme using microlens arrays as screen material for application in laser-based projection systems. The scheme is based on properly adjusting the coherence properties on the screen: when the coherence area on the microlens-array screen is smaller than the microlens footprint, there is no interference between the fields emitted by the different microlenses and as a result no speckle is formed. We measured and modelled the speckle properties of microlens arrays with regular and irregular structure and lens sizes, and also a paper screen for comparison. In the experiments, we tune the laser beam's spatial coherence by sending it through a rotating diffuser. We show the amount of speckle reduction that can be achieved, which mechanisms influence the observed speckle contrast and we discuss the limitations due to increased non-uniformity in the projected image.