Ground-state emission wavelengths of pyramidal In As quantum dots (QDs) with a base length of b and a height of h capped by composite InGaAs and InAlAs layers were investigated theoretically in a one-band effective mass model framework. It was found that the ground-state emission wavelengths depend not only on the h/b ratio, but also on the thickness and position of the InGaAs and InAlAs layers. The maximum transition energy separation between the QD ground-and first-excited states appears in the composite InGaAs and InAlAs layers, but not on a single InGaAs or InAlAs overgrown layer. Such a result is attributed to the degree of delocalization for the first excited state being different from that of the ground state.