Several species of birds lay second eggs that are eliminated by the siblicidal behavior of the first-hatched chick. A widely accepted explanation for the occurrence of these second eggs is insurance against complete nest failure. However, if insurance is seen as an important breeding strategy for two-egg (c/2) layers, the question arises why single-egg species do not lay insurance eggs. The insurance-egg hypothesis predicts that extra eggs should occur where hatch failure is not trivial, which may be particularly prevalent in dense populations. Neither prediction was supported for siblicidal l Wahlberg's eagles Aquila wahlberge Neither could food constraints or allometric relationships explain the small one-egg clutch (c/1) of this species Instead, clutch size was experimentally shown to be related to optimal brood size: parents given two young were unable to rear them, and subsequent breeding opportunities were significantly curtailed. Since clutch and brood size are similarly related in c/2 eagles, insurance may be an exaptation of the second egg. One-egg spedes, however, appear to trade second (insurance) eggs for large, high-quality eggs, which enhance hatchability and chick viability. This was borne out by comparison of the world's c/1 eagles, which lay significantly (p<.01) larger eggs than c/2 eagles of the same body size. Large Wahlberg's eagle eggs also showed significantly (p=.02) greater hatchability than small eggs, and other studies show enhanced survival/quality for chicks from large eggs. Because only longer-lived eagles traded two eggs for single, large eggs, this is consistent with the idea of selection for offspring quality in long-lived species. I condude that higher hatchability of single, large eggs decreases the need for an insurance egg and simultaneously enhances viability of resultant chicks in sibliddal eagles and possibly sulids.