  Stochastic inflation can resolve strong inflationary perturbations, which
seed primordial black holes. I present a fast and accurate way to compute these
perturbations in typical black hole producing single-field models, treating the
short-wavelength Fourier modes beyond the de Sitter approximation. The
squeezing and freezing of the modes reduces the problem to one dimension, and
the resulting new form of the stochastic equations, dubbed `constrained
stochastic inflation,' can be solved efficiently with semi-analytical
techniques and numerical importance sampling. In an example case, the
perturbation distribution is resolved in seconds deep into its non-Gaussian
tail, a speed-up of factor $10^9$ compared to a previous study. Along the way,
I comment on the role of the momentum constraint in stochastic inflation.
