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P-Compatibility is a hereditary property of identities which generalizes the properties of normality and exteality of identitiesChajda characterized the normalization of a variety by an algebraic construction called a choice algebraIn this paper, we generalize this characterization to the least P-compatible variety P(V) determined by a variety V for any partition P using P-choice algebrasWe also study the clone of (strongly) P-compatible n-ary terms of a variety V, and relate identities of this clone to (strongly) P-compatible hyperidentities of the variety V.