Stochastic inflation resolves primordial perturbations nonlinearly, probing their probability distribution deep into its non-Gaussian tail. The strongest perturbations collapse into primordial black holes. In typical black-hole-producing single-field inflation, the strongest stochastic kicks occur during a period of constant roll. In this paper, I solve the stochastic constant-roll system, drawing the stochastic kicks from a numerically computed power spectrum, beyond the usual de Sitter approximation. The perturbation probability distribution is an analytical function of the integrated curvature power spectrum σk2 and the second slow-roll parameter ϵ2. With a large ϵ2, stochastic effects can reduce the height of the curvature power spectrum required to form asteroid mass black holes from 10-2 to 10-3. I compare these results to studies with the nonstochastic ΔN formalism.