It has already been shown how to obtain 2-speed single-winding squirrel-cage induction motors, using a normal stator with all coils identical, and with only six terminals to the winding. The earlier methods showed how an integral-slot winding may be modulated to give a 2-speed winding for any pole combination, and also how to design a fractional-slot 2-speed winding for pole combinations which do not include a multiple of 6. The fractional-slot windings are the best, and this paper completes the record of close-ratio pole-amplitude modulation in its basic form by showing how to design a fractional-slot winding for any close-ratio pole combination.The performance of machines with such fractional-slot windings very nearly approaches that of a single-speed motor, for both speeds; and it is thought that, for most applications, these fractional-slot windings will supersede the earlier integral-slot ones. Tables of finished winding designs for one pole combination are given in full, together with details of the design methods, which are illustrated by the complete working of one particular design. The basic part of the task of converting the single-winding squirrel-cage induction motor into a close-ratio 2-speed machine has therefore been completed and recorded in full. The application of the same principles to wide-ratio 2-speed machines has been separately described, as will also be certain further developments of the work already recorded.