Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $φ$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we pinpoint three concerns about $φ$ and propose a revised measure, $ψ$, which addresses them. Our measure $ψ$ is rigorously grounded in Partial Information Decomposition and is faster to compute than $φ$.