Potential heuristics assign numerical values (potentials) to state features, where each feature is a conjunction of facts. It was previously shown that the informativeness of potential heuristics can be significantly improved by considering complex features, but computing potentials over all pairs of facts is already too costly in practice. In this paper, we investigate whether using just a few high-dimensional features instead of all conjunctions up to a dimension n can result in improved heuristics while keeping the computational cost at bay. We focus on (a) establishing a framework for studying this kind of potential heuristics, and (b) whether it is reasonable to expect improvement with just a few conjunctions. For (a), we propose two compilations that encode each conjunction explicitly as a new fact so that we can compute potentials over conjunctions in the original task as one-dimensional potentials in the compilation. Regarding (b), we provide evidence that informativeness of potential heuristics can be significantly increased with a small set of conjunctions, and these improvements have positive impact on the number of solved tasks.