Fluorescence microscopy images are inevitably tainted by background contributions including emission from out-of-focus planes, scattered light, and detector noise. In stimulated emission depletion (STED) nanoscopy, an additional, method-specific background arises from incomplete depletion and re-excitation by the depletion beam. Various approaches have been proposed to remove the background from a STED image, some of which rely on the acquisition of a separate background image that is subtracted from the STED image with a weighting factor. Using stimulated emission double depletion (STEDD) nanoscopy, we observed that the weighting factor varies locally in densely labeled samples, so that background removal with a single (global) weighting factor generates local image artifacts due to incorrect background subtraction. Here we present an algorithm that computes the optimal weighting factor at the single-pixel level, yielding a difference image with excellent suppression of low-frequency background.