We study Bernoulli percolation on $\mathbb{Z}^d$, in dimensions $d>6$. We prove that a classical consequence of the van den Berg–Kesten inequality, often referred to as the Simon–Lieb inequality in the context of the Ising model, admits a partial reversal. As a main application, we prove that, at criticality, the expected number of pioneers of a set $S$ containing the origin (i.e. boundary vertices connected to the origin within $S$) is bounded uniformly in $S$. This result was previously known only for boxes and half-spaces. This partial reversal further yields a short and self-contained route to several key results, including near-critical estimates on the two-point function and sharp bounds on the critical one-arm probability. Joint work with Bruno Schapira.