Cross-sectional scanning tunneling microscopy was used to study at the atomic scale the double capping process of self-assembled InAs/InP quantum dots (QDs) grown by molecular beam epitaxy on a (311)B substrate. The thickness of the first capping layer is found to play a mayor role in determining the final results of the process. For first capping layers up to 3.5 nm, the height of the QDs correspond to the thickness of the first capping layer. Nevertheless, for thicknesses higher than 3.5 nm, a reduction in the dot height compared to the thickness of the first capping layer is observed. These results are interpreted in terms of a transition from a double capping to a classical capping process when the first capping layer is thick enough to completely cover the dots.