A continuous, analytical model of the selection of size-number compromises is presented and applied to the selection of the amount of parental investment in each offspring until its independence. At the evolutionarily stable strategy, the proportional gain in the success of an offspring from an increment in the investment in the offspring equals the proportional loss in offspring numbers. A parallel marginal-value theorem applies to discontinuous variation in the amount of care. When selection acts directly on offspring size rather than on number, the evolutionarily stable level of care depends only on the fitness curve relating the fitness of single offspring to the amount of resources received. General conditions for brood reduction are described. A more-specific rapid-gain version of the continuous model suggests that the amount of parental care is influenced primarily by the level of care at which offspring success increases rapidly. The model can explain various observed differences in amounts of parental care, such as those of r-selected versus K-selected species. The work of an unrecognized predecessor of r- and K-selection theory, E. J. Salisbury, is acknowledged. There are many other size-number compromises, including those for repeated plant structures and for the number of broods per year and other "packaging" strategies, to which models paralleling those for parental strategies can be applied.