Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y = 1|x), where x is a vector (template) of observed values in the observation window and Y is the value in the image to be estimated by the filter. The optimal window filter is defined by y(x) = 1 if P(Y = 1|x) > 0.5 and y(x) = 0 if P(Y = 1|x) 0.5, which is the binary conditional expectation. The fundamental problem of filter design is to estimate P(Y = 1|x) from data (image realizations), where x ranges over all possible observation vectors in the window. A Bayesian approach to the problem can be employed by assuming, for each x, a prior distribution for P(Y = 1|x). These prior distributions result from considering a range of model states by which the observed images are obtained from the ideal. Instead of estimating P(Y = 1|x) directly from observations by its sample mean relative to an image sample, P(Y = 1|x) is estimated in the Bayesian fashion, its Bayes estimator being the conditional expec tation of P(Y = 1|x) given the data. Recently the authors have shown that, with accurate prior information, the Bayesian multiresolution filter has significant benefits from multiresolution filter design. Further, since the Bayesian filter is trained over a wider range of degradation levels, it inherits the added benefit of filtering a degraded image at different degradation levels in addition permitting iterative filtering. We discuss the necessary conditions that make a binary filter a good iterative filter and show that the Bayesian multiresolution filter is a natural candidate. The basic idea behind Bayesian iterative filtering is that, since the prior distribution covers a wide range of degradation levels, an application of the filter converts the degraded image to an image of less degradation for which the prior distribution is sufficiently robust to still be effective. Further application of the filter leads to further reduction of degradation. We consider edge noise in the experiments, with an emphasi s on realistically degraded document images.