A pump sleeve for an inversion pump in an integrated drive generator has a pump sleeve body extending between a first end and a second end, the first end being at a location adjacent an enlarged endplate. The body extends to the second end with a generally cylindrical body portion having a bore of an inner diameter from the first end to the second end, and between the first and second ends for a distance. A ratio of the first distance to the inner diameter being is 1.8 and 2.0. In addition, an integrated drive generator is disclosed as is a method of replacing an accessory drive gear in an integrated drive generator.