A method of lubricating a coupling shaft of a gear pump includes communicating lubricant from a first gear stage along a first splined end section of the coupling shaft and through a first slot in a first radial shoulder of the coupling shaft, and also communicating lubricant from a second gear stage along a second splined end section of the coupling shaft and through a second slot in a second radial shoulder of the coupling shaft. The first radial shoulder is axially spaced from the second radial shoulder by an axial distance SA along an axis of rotation of the coupling shaft. The first and second slots each define a lowermost radial dimension SR from the axis of rotation, with a ratio SR/SA of 0.25-0.77.