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This paper explores the optimal design of power and spectrally efficient coded modulations based on amplitude phase shift keying (APSK) with application to satellite communications. Focal point is put on 32-APSK constellations. We optimize the 32-APSK constellation design by using an optimization criterion based on the mutual information at first. Two separate cases are particularly examined: (i) the equiprobable case and (ii) the non-equiprobable case. After obtained the optimal results, we change the value of the phase shift to get a better error performance. Following this optimization approach, detailed simulation results are obtained for the optimal 32-APSK constellation settings, the available shaping gain as well as the error performance.