Answer set programming (ASP) and conditional reasoning are powerful KR formalisms capable of expressing default statements that usually hold but also allow for exceptions. While ASP excels with an intuitive rule-based syntax, fast solvers, and is suited to solve complex combinatorial search problems, conditionals provide a sophisticated preference-based semantics and yield principled inferences. In this paper, we investigate and compare different computational approaches on utilizing conditional background knowledge in order to prioritize the solutions of ASP programs. For this, we compile the specification of the System Z ranking model of conditionals into ASP constraints and, therewith, integrate the guidelines for prioritization according to System Z directly into the ASP programs.