The use of thin AlA capping layers (CLs) on InAs quantum dots (QDs) has recently received considerable attention due to improved photovoltaic performance in QD solar cells. However, there is little data on the structural changes that occur during capping and their relation to different growth conditions. In this work, we studied the effect of AlA capping growth rate (CGR) on the structural features of InAs QDs in terms of shape, size, density, and average content. As will be shown, there are notable differences in the characteristics of the QDs upon changing CGR. The Al distribution analysis in the CL around the QDs was revealed to be the key. On the one hand, for the lowest CGR, Al has a homogeneous distribution over the entire surface, but there is a large thickening of the CL on the sides of the QD. As a result, the QDs are lower, lenticular in shape, but richer in In. On the other hand, for the higher CGRs, Al accumulates preferentially around the QD but with a more uniform thickness, resulting in taller QDs, which progressively adopt a truncated pyramidal shape. Surprisingly, intermediate CGRs do not improve either of these behaviors, resulting in less enriched QDs.