The authors propose a suboptimal algorithm for adaptive subcarrier, bit and power allocation for orthogonal frequency division multiple access-based spectrum-sharing networks. This problem in its original form is non-convex and may be solved using greedy algorithms or integer linear programming (ILP) techniques. However, the computational complexity of the latter techniques is quite high, while the suboptimal greedy algorithms are not very well suited for spectrum-sharing networks because of multiple constraints on the transmitted power, interference leakage and individual user data rate. Therefore the authors propose a novel recursion-based linear optimisation framework that provides a solution that is very close to the optimal one and that has the ability to perform adaptive subcarrier, bit and power allocation for multiple users in the presence of multiple individual user constraints. Owing to the convexity of the proposed algorithm at each recursion, its overall complexity is substantially lower than that of the ILP-based solution.