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This paper analyzes restoration of subtractive noise on a binary image by a single morphological operation, dilation. Restoration by dilation alone is appropriate under particular explicitly defined random noise models, based respectively on erosion, independentpixel subtractive noise, and independent pixel subtractive noise followed by dilation. Since in general it is not possible to perfectly restore subtractive noise we use the Hausdorf metric to measure the residual error in restoration. This metric is the appropriate one because of its geometric interpretation in terms of set coverings.We describe a search procedure to find a structuring element for dilation that is optimal in the sense of minimizing the mean Hausdorf error. The search procedure's utility function is based on the calculation of certain probabilities related to the noise model, namely the probability of one set being the subset of another set and some related probabilities.