A way of generating simple derivatives from H. Caswell's (1978, Theor. Pop. Biol. 14, 215–230) population growth rate sensitivity measure is described that allows the analysis of pleiotropism involving modifications of an arbitrary number of life history parameters. Some cases are investigated that show that the precise nature of the pleiotropic constraints is critical in determining whether or not a new life history trait will be favored, thereby making it difficult to identify a single optimal life history. Caswell's measure is then generalized to cases in which the stable age distribution does not hold, a situation more applicable to many r-selected species.