Heuristic functions based on the delete relaxation compute upper and lower bounds on the optimal delete-relaxation heuristic h+, and are of paramount importance in both optimal and satisficing planning. Here we introduce a principled and flexible technique for improving h+, by augmenting delete-relaxed planning tasks with a limited amount of delete information. This is done by introducing special fluents that explicitly represent conjunctions of fluents in the original planning task, rendering h+ the perfect heuristic h* in the limit. Previous work has introduced a method in which the growth of the task is potentially exponential in the number of conjunctions introduced. We formulate an alternative technique relying on conditional effects, limiting the growth of the task to be linear in this number. We show that this method still renders h+ the perfect heuristic h* in the limit. We propose techniques to find an informative set of conjunctions to be introduced in different settings, and analyze and extend existing methods for lower-bounding and upper-bounding h+ in the presence of conditional effects. We evaluate the resulting heuristic functions empirically on a set of IPC benchmarks, and show that they are sometimes much more informative than standard delete-relaxation heuristics.