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We study the problem of allocating subchannels, bits, and powers for variable rate services in an OFDM based cognitive radio (CR) system, in which available system resources are highly dynamic. 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 simulation results are obtained which show that the proposed distributed algorithm provides good fairness and aggregate bit rates close to (within 8% of) optimal values.