In this paper, we address the problem of multiple access interference (MAI) in a downlink multicarrier code division multiple access system. Because in the realistic case of correlated faded subcarriers, MAI greatly depends on the codes assigned to users, one way of improving performance without increasing receiver complexity consists in an appropriate code selection. We propose a code allocation strategy with the following properties: possible use with any code sequence and equalizer, low complexity, and efficient management of load variations. The allocation problem is formulated as a minimization problem of a cost function related to MAI. First, we provide analytical expressions for the channel frequency correlation function after maximum ratio combining, equal gain combining, and minimum mean square error equalization and for the MAI power. Then, by approximating these expressions, we define a simple cost function and build an iterative algorithm on the basis of the minimum maximum criterion to select the spreading codes. Finally, a complete analysis of the allocation efficiency is provided versus key parameters, in particular, the degree of correlation between the faded subcarriers, the system load, and the equalization techniques.