This paper formulates and compares procedures for reducing computation in carrying out m-step or polynomial preconditioning in the conjugate gradient method. These procedures are based on corresponding ones for one-step preconditioning given by Bank and Douglas [Appl. Numer. Math., 1(1985), pp. 489–492], Conrad and Wallach [Numer. Math., 27 (1979), pp. 371–372], and Eisenstat [SIAM J. Sci. Statist. Comput., 2 (1981), pp. 1–4], and apply, in particular, to SSOR preconditioning. Comparisons are made based on operation counts, storage, and parallel and vector properties, and it is concluded that the Eisenstat procedure is the most effective. Numerical experiments on a parallel computer are also given.