The relationship between pleiotropy and the rate of evolution of a phenotypic character (evolvability) in a population is explored using computer simulations. I present results that suggest the rate of evolution of a phenotypic character may not decline when that character is pleiotropically associated to an increasing number of other characters, provided that the characters are under pure directional selection such that they are far from their optima relative to the average magnitude of a mutation. These conditions may be relevant during adaptive radiations. Adding pleiotropic associations to a set of characters in which one is under directional selection and the other is under stabilizing selection increases the rate of adaptation of the character under directional selection provided that the new characters that come to be pleiotropically associated are under directional selection. Thus, increasing the number of pleiotropic associations under these conditions increases the rate of adaptation of a character.