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We consider the problem of scheduling multicarrier wireless data in systems such as IEEE 802.16 (WiMAX). Each scheduling decision involves assigning carriers to users for each time slot, subject to the constraint that each carrier is assigned to at most one user, but multiple carriers can potentially be assigned to the same user. One important aspect of our problem is that a scheduler knows the channel rates across all users and all carriers whenever a scheduling decision is made. This “global” information may give a potential for enhancing performance via an optimized allocation of carriers to users. We analyze this problem in a situation where finite queues are fed by a data arrival process. The well-known MaxWeight algorithm for the single-carrier setting maximizes the product of queue size and service rate. We focus on how to adapt MaxWeight to the multicarrier setting. If the same objective is pursued, more service than needed may be assigned to drain a queue, thereby creating wastage. While a simple variant in the objective forbids this wastage, it turns an easy-to-compute old objective into an intractable new objective. We state the hardness of the new optimization problems and propose several extremely simple algorithms with provable performance bounds. We conclude with supporting simulation examples.