Abstract. The goal of partial evaluation is the specialization of programs w.r.t. part of their input data. Although this technique is already well-known in the context of functional languages, current approaches are either overly restrictive or destroy sharing through the specialization process, which is unacceptable from a performance point of view. In this work, we present the basis of a new partial evaluation scheme for first-order lazy functional programs that preserves sharing through the specialization process and still allows the unfolding of arbitrary function calls.