An advanced pairing correction for an existing formula of particle-hole state densities, needed in calculations of cross sections with the precompound nuclear reaction theory, is examined. The Pauli correction is derived to be consistent with this pairing correction. The accuracy of the pairing correction plus the Pauli correction is shown to be sufficient for applied calculations. Numerical solutions of the pairing equations, needed for generating the corrections, have been carried out. The relevant numerical results are presented as simple functions of the excitation energy and the exciton number. A relationship between the pairing correction for particle-hole state densities and the pairing correction for the total state densities in the closed-form formulation is developed. Utilization of the existing level-density parameters and data for deducing parameters for the particle-hole state densities are shown.