A numerical study is made on the ducted-whistler propagation in the magnetosphere by using the phase-integral technique. The guidance in the present model takes place along a dipole field-aligned irregularity with a slowly varying, quartic distribution of ionization density. Numerical calculations are made on the track widths, the mode angles, and the travel times of trapped modes for a wide range of irregularity parameters. Calculations are carried out for a field line for which the shell parameter L=2, Angerami and Thomas's model of ionization density being employed as a background component of the plasma distribution. It is shown that an increase in the transverse size of irregularity may not be responsible for the increase in whistler diffuseness.