We introduce a simple variation of the additive heuristic used in the HSP planner that combines the benefits of the original additive heuristic, namely its mathematical formulation and its ability to handle non-uniform action costs, with the benefits of the relaxed planning graph heuristic used in FF, namely its compatibility with the highly effective enforced hill climbing search along with its ability to identify helpful actions. We implement a planner similar to FF except that it uses relaxed plans obtained from the additive heuristic rather than those obtained from the relaxed planning graph. We then evaluate the resulting planner in problems where action costs are not uniform and plans with smaller overall cost (as opposed to length) are preferred, where it is shown to compare well with cost-sensitive planners such as SGPlan, Sapa, and LPG. We also consider a further variation of the additive heuristic, where symbolic labels representing action sets are propagated rather than numbers, and show that this scheme can be further developed to construct heuristics that can take delete-information into account.