Slotted axial-flux machines have excellent power and torque densities. However, it is difficult to reduce their cogging torque due to the complexity associated with implementing classical techniques. In this paper, slot-opening widths and tooth profiles will be shown to be significant in mitigating cogging torque in these machines. In particular, varying the slot opening reduced it by 52%, whereas a parallel-tooth (rectangular) profile lowered it by 24%, when compared with a conventional trapezoidal-tooth profile. An analytical quasi-3-D analysis was formulated and used to analyze and determine cogging torque. It was validated numerically and experimentally. Its versatility is in its ability to analyze different shapes of poles and slot openings, which can be extended to model air-gap nonuniformity. This paper also presents cogging torque minimization techniques that maintain the ease of manufacture of the parallel-tooth stator. Experimental results showed 73% and 48% reduction in cogging torque, which are achieved by the use of alternating pole arcs and skewed poles.