A logical first step toward incorporating a precompound nuclear reaction theory in the Hauser-Feshbach formalism, widely used for compound reaction cross-section calculations, is to develop unified level density formulas needed for the two parts of the calculation. An advanced, simplified formulation of the spin cutoff factors for particle-hole level densities, based on the uniform pairing model, is presented. This simplified formula, explicitly dependent on the excitation energy and the exciton number, is easy to use for the precompound part of the calculation and is shown to be consistent with the formula used for the Hauser-Feshbach part of the calculation. Differences between the present approach and a previous one are analyzed.