Summary form only given. The predicted improved performance of a semiconductor laser with active regions based on quantum dots (QDs) is presently being explored in many laboratories. One of the major issues is to investigate how a discrete energy level in the QD can be populated, if the spacings to other levels do not match the LO phonon energy. We show, that even though the level structure of the quantum dot does not allow carrier transitions between the levels mediated by LO phonons, the elastic scattering of LO phonons on the confined carriers is an efficient dephasing mechanism. Our calculations show that the dephasing results in a homogeneous linewidth of the order of 6 meV, which is consistent with recent experimental findings. A similar approach has been used to explain the line broadening in doped crystals.