The authors study the dependence of neoclassical diffusion coefficients in solenoids wound round a circular torus on the modulation of the helical magnetic axis of traps of this kind. They consider the regime where the effective trapped-particle collision frequency is higher than the frequency of precession of the bananas around the magnetic axis, but much lower than the frequency of trapped-particle oscillations between the magnetic mirrors. It is demonstrated that there is an optimal modulation of the helical magnetic axis at which the diffusion coefficients prove to be minimal.