In this paper we explore the challenges surrounding searching effectively in problems with preferences. These problems are characterized by a relative abundance of goal states: at one extreme, if every goal is soft, every state is a goal state. We present techniques for planning in such search spaces, managing the sometimes-conflicting aims of intensifying search around states on the open list that are heuristically close to new, better goal states; and ensuring search is sufficiently diverse to find new low-cost areas of the search space, avoiding local minima. Our approach uses a novel cost-bound-sensitive heuristic, based on finding several heuristic distance-to-go estimates in each state, each satisfying a different subset of preferences. We present results comparing our new techniques to the current state-of-the-art and demonstrating their effectiveness on a wide range of problems from recent International Planning Competitions.