We present a new continuity correction to the P value for local maxima of a statistical parametric map that bridges the gap between small FWHM, when the Bonferroni correction is accurate, and large FWHM, when random field theory is accurate. The new method, based on discrete local maxima, is always an upper bound (like the Bonferroni), but lower and hence more accurate for large FWHM, without increasing false positives. It resulted in P values that were approximately 43% lower than the best of Bonferroni or random field theory methods when applied to a typical fMRI data set.