Microphotoluminescence spectroscopy at variable temperature, excitation intensity, and energy was performed on a single InAs/AlAs self-assembled quantum dot. The exciton emission line [zero-phonon line (ZPL)] exhibits a broad sideband due to exciton acoustic-phonon coupling by the deformation-potential mechanism. Additionally, narrow low-energy sidebands at about 0.25 meV of the ZPL are attributed to exciton acoustic-phonon piezoelectric coupling. In lowering the excitation energy or intensity these bands gradually dominate the emission spectrum of the quantum dot while the ZPL disappears. At high excitation intensity the sidebands due to piezoelectric coupling decrease strongly and the ZPL dominates the spectrum as a consequence of screening of the piezoelectric coupling by the photocreated free carriers.