Monte Carlo computer simulations were carried out in order to compare unrestricted phenotypic and restricted combined‐index selection, applied over one generation of single‐pair mating, for a wide range of family sizes and heritabilities, and for two sizes of breeding populations. The simulations demonstrate that when restrictions are imposed to control reduction of diversity to equivalent population size (status number), there are situations where phenotypic selection will achieve greater gain than that achievable by combined‐index selection. On average, unrestricted phenotypic selection was found to be similar to or better than restricted combined‐index selection at the same status number for heritabilities higher than 0.2. For lower heritabilities, phenotypic selection was less efficient. Selection in larger families resulted in greater gain, but at the expense of genetic diversity. Unrestricted phenotypic selection often proved to be a more efficient method, preserving more genetic diversity per unit gain. Restricting the number of selections per family is an efficient method to balance gain and diversity after combined‐index selection. The size of the breeding population appeared to have a minor effect on gain, but can affect the rate at which overall genetic diversity is eroded.