Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E . If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L ≥ 1 , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T .