Conditional preference networks (CP-nets) have received significant attention for modeling preferences over combinations of features. However, dominance testing, the problem of inferring from a CP-net whether one outcome is always preferred over another, is NP-hard, requiring exponential time in practice. In this paper, we introduce the use of independent relaxed subproblems as a heuristic for faster inference from CP-nets. We show how to relax the constraints in the conditional preference tables and partition the network, yielding smaller subproblems that can be solved easily. The lengths of these solutions can then be added together to provide a heuristic for informed search algorithms such as A* and applied to dominance testing in CP-nets. We prove that the resulting additive heuristic function is admissible and consistent, guaranteeing optimality and completeness. We show from experiments on randomly generated binary and multivalued CP-nets that our method performs better than the state of the art, and can further be combined with other pruning techniques, resulting in greatly improved performance for dominance testing.