We consider scheduling and resource allocation for the downlink of a cellular OFDM system, with various practical considerations including integer tone allocations, different sub-channelization schemes, maximum SNR constraint per tone, and "self-noise" due to channel estimation errors and phase noise. During each time-slot a subset of users must be scheduled, and the available tones and transmission power must be allocated among them. Employing a gradient-based scheduling scheme presented in earlier papers reduces this to an optimization problem to be solved in each time-slot. Using a dual formulation, we give an optimal algorithm for this problem when multiple users can time-share each tone. We then give several low complexity heuristics that enforce integer tone allocations. Simulations are used to compare the performance of different algorithms.