Observations of young clusters indicate that a significant fraction of solar-type stars are rotating very slowly, with equatorial velocities less than 10 km s-1. So far, models have failed to reproduce a sufficiently large proportion of these stars on the zero-age main sequence. On the basis of the idea that the mixing length in convection theories could depend on the size of the convective zone (Canuto & Mazzitelli), we examine the influence of a varying mixing-length parameter α on the rotational evolution of solar-type stars. A decreasing α (owing to evolution) in the mixing-length theory (MLT) leads to a slower contraction rate and to a larger stellar moment of inertia. The stellar spin-up is consequently reduced, and this helps to increase the number of very slow rotators present in young clusters. We also investigate the possibility that α could depend on the rotation rate, and show the consequences of this parameterization for the lithium surface abundance.