It is shown that structural similarity between proteins can be decided well with much less information than what is used in common similarity measures. The full C representation contains redundant information because of the inherent chain nature of proteins and a limit on the compactness due to excluded volume. A wavelet analysis on random chains and proteins suggests approximating subchains by their centers of mass. For not too compact chain-like structures in general, and proteins in particular, similarity measures that use this approximation are highly correlated to the exact similarity measures and are therefore useful, e.g. as fast filters. Experimental results with such simplified similarity measures in two applications, nearest neighbor search and automatic structural classification show a significant speed up.