This paper illustrates a method of studying changes in vital rate schedules which have no effect on the intrinsic rate of population growth. These changes are described as compensating changes in fertility and mortality. The analysis proceeds from the discrete perspective of Leslie matrices, wherein the central idea is to establish the set of all compensating changes by identifying that class of Leslie matrices which possess the same positive eigenvalue, λ1. A root-squaring technique is adapted for the purpose of estimating λ1. Finally, a variety of compensating fertility and mortality changes is illustrated using data from Japan.