The invention relates to a filter for filtering media, having a pleated, cylindrical filter element which is arranged between a perforated cylindrical backflow prevention device and a perforated cylindrical core, wherein the filter element is arranged in pleated folds, wherein a plurality of folds have a first fold height which is greater than the difference between the radius of the backflow prevention device and the radius of the core, said folds being inclined, in a manner directed away from the outer surface of the core, at an inclination angle in each case with respect to a radial line, wherein a plurality of folds at least of a second, shorter fold height are provided and wherein the folds of the second, shorter fold height are arranged adjacent to the backflow prevention device radially towards the outside and adjacent in an alternating manner to the folds of the first fold height.