Thresholding converts a greyscale image into a binary image, and is thus often a necessary segmentation step in image processing. For a human viewer however, thresholding usually has a negative impact on the legibility of document images. This report describes a simple method for "smearing out" the threshold and transforming the greyscale image into a different greyscale image. The method is similar to fuzzy thresholding, but is discussed here in the simpler context of greyscale transformations and, unlike fuzzy thresholding, it is independent from the method for finding the threshold. A simple formula is presented for automatically determining the width of the threshold spread. The method can be used, e.g., for enhancing images for the presentation in online facsimile repositories.