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We give a general technique for constructing a functorial choice of very goodpaths objects, which can be used to implement identity types in models of typetheories in direct manner with little reliance on general coherence results. Wegive a simple proof that applies in algebraic model structures that possess anotion of structured weak equivalence, in a sense that we define here. We thengive a more direct proof that applies both to the original BCH cubical setmodel and more recent variants. We give an explanation how this constructionrelates to the one used in the CCHM cubical set model of type theory.

Identity Types in Algebraic Model Structures and Cubical Sets