Williams (1966; Am. Nat. 100(916): 687–690) furthered R.A. Fisher’s concept of reproductive value by breaking it into two components: (1) current reproduction and (2) residual reproductive value (RRV, the summed product of survival and reproduction over the rest of the lifespan). He predicted a negative correlation of measures of these two components among species, and this prediction led in part to the idea of trade-offs in life-history theory. We tested Williams’ prediction with 24 species of albatrosses and petrels (order Procellariiformes), species with a great range of body sizes and all laying only one egg at a time (like humans, highly iteroparous). Two measures of reproductive investment were not negatively correlated with RRV. Adjusting data for body mass and phylogeny resulted in significant positive associations. In addition, any measure of annual parental allocation to reproduction (once adjusted for body size) should give a positive association with RRV as shown by a simple simulation model that assumes a highly iteroparous life cycle. Under such life cycles, Williams’ prediction confounds the positive influence of reproduction on both current investment and RRV. Principles of life-history theory, however, do not require re-evaluation, as this particular prediction can in at least some cases be internally inconsistent.