We study carrier assignment in a single-cell multiuser OFDM multi-carrier system so as to satisfy user rate requirements with minimal resources. Different users experience different quality in different carriers due to frequency selectivity of users' propagation channels and due to non-co-located user receivers that perceive different interference from neighboring cells across carriers. We study a static instance of the problem, specified by user carrier qualities and rate requirements. Adaptive modulation at the transmitter differentiates carriers for each user. In good quality carriers, the user satisfies per-frame rate requirements with few slots (or equivalently it satisfies its per-slot rate requirements with small occupied time slot portion). We study integral and fractional assignment, where a user is assigned to only one or several carriers. Fractional assignment is formulated as a linear programming problem. For integral assignment, we introduce two classes of iterative heuristics that use carrier reassignment to users and user substitution in carriers respectively and may be viewed as resulting from corresponding optimal fractional assignment algorithms. We use Lagrangian relaxation to obtain performance bounds and show that the two classes of heuristics arise from two relaxations. Our approach identifies efficient feasible solutions and is amenable to distributed implementation.