The peak power of high-power laser facilities is limited by the laser-induced damage to the final optical components. Also, when a damage site is generated, the damage growth phenomenon limits the lifetime of the component. Many studies have been performed to improve the laser-induced damage threshold of these components. The question now arises as to whether improvement of the initiation threshold leads to a reduction of the damage growth phenomenon. To address this question, we performed damage growth experiments on three different multilayer dielectric mirror designs exhibiting different damage thresholds. We used classical quarter-wave designs and optimized designs. The experiments were carried out with a spatial top-hat beam, spectrally centered at 1053 nm with a pulse duration of 0.8 ps in s- and p-polarization. The results showed the impact of design on the improvement of the damage growth thresholds and a reduction of the damage growth rates. A numerical model was used to simulate damage growth sequences. The results reveal similar trends to those observed experimentally. On the basis of these three cases, we have shown that improvement of the initiation threshold through a modification of the mirror design can lead to the reduction of the damage growth phenomenon.