In this paper, new interleaver design criteria for turbo codes are proposed, targeting the reduction of the correlation between component decoders. To go beyond the already known correlation girth maximization, we propose several additional criteria that limit the impact of short correlation cycles and increase code diversity. Two application examples are elaborated, targeting an 8-state binary turbo code and a non-binary turbo code defined over GF(64). The proposed design criteria are shown to improve the error correcting performance of the code, especially in the error floor region.