We study the problem of allocating subchannels, bits, and powers in a cognitive radio system, in which available system resources are highly dynamic. The modulation scheme employed is orthogonal frequency-division multiplexing (OFDM). In a resource-limited situation under which the nominal-rate requirements of users cannot be satisfied, it is desirable to provide fair degradation among users. In a situation with abundant resources, we may choose to maximize system throughput while ensuring that user nominal-rate requirements are met. The problem is formulated as a single objective nonlinear optimization problem using techniques from goal programming. A distributed resource allocation algorithm is proposed and shown to provide good fairness. In resource-abundant situations, the proposed distributed algorithm yields significantly better system throughput compared with the proportional-rate algorithm.