We present a method for reducing the cogging force in axially magnetized tubular permanent-magnet machines. The method consists of placing several similar slots on the iron pole-pieces. By choosing the appropriate positions of the pole-piece slots, specific harmonics of the cogging force can be eliminated, and, as a result, the cogging force may be greatly reduced. To obtain a general expression for the positions of the iron pole-piece slots, we use harmonic analysis with Fourier series. We demonstrate the validity of the cogging force reduction technique by finite-element analysis.