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Abstract. KiCS2 is a new system to compile functional logic programs of the source language Curry into purely functional Haskell programs. The implementation is based on the idea to represent the search space as a data structure and logic variables as operations that generate their values. This has the advantage that one can apply various, and in particular, complete search strategies to compute solutions. However, the generation of all values for logic variables might be inefficient for applications that exploit constraints on partially known values. To overcome this drawback, we propose new techniques to implement equational constraints in this framework. In particular, we show how unification modulo function evaluation and functional patterns can be added without sacrificing the efficiency of the kernel implementation.