This paper develops a theoretical model for analyzing gene bank management decisions regarding the search for traits of economic value in ex situ collections of wheat. The model is applied to data on the probability of finding useful sources of resistance to Russian wheat aphid (Diuraphis noxia) and septoria tritici leaf blotch, using Monte Carlo simulations for sampling distributions, simulations of varietal diffusion paths, and actual cost data from searches. Three specific questions are posed and answered: (1) what is the optimal size of search among genetic resources of a given type for a trait of economic value? (2) what is the value of specialized knowledge about which genetic resources are most likely to display resistance? and (3) how should search resources be allocated across types of genetic resources? Results demonstrate the sensitivity of the optimal size of search to the economic importance of the problem, the probability distributions of the trait in different types of genetic resources, and the costs and time lags associated with transferring the trait into usable breeding material. The costs and time lags involved with conventional pre-breeding techniques imply that in some searches, certain categories of genetic resources (such as landraces) will be systematically ignored. The fact that they may be rarely utilized does not imply that collections of landraces have no value, however, as shown in the case of Russian wheat aphid. Though applied here to data on insect and disease resistance, the model can be adapted to search decisions for other types of traits.