We develop and test a direct method for computing two-particle excess entropies in the canonical ensemble. The method is based on a systematic expansion of the entropy into one-body, two-body, three-body, etc., contributions. Unlike earlier canonical ensemble methods the resulting expressions for the entropy are local. It is shown that, at liquid densities, the three-body (and higher) terms are small but not negligible. The largest discrepancies are found at intermediate densities.