Before revision:  We investigate the synergies between sparse regression solvers and basis adaptivity schemes, and provide recommendations on which of them are most promising for specific classes of problems.
After revision:  We investigate the synergies between sparse regression solvers and basis adaptivity schemes, we find that virtually all basis-adaptive schemes outperform a static choice of basis. Three sparse solvers, namely Bayesian compressive sensing and two variants of subspace pursuit, perform especially well. Aggregating our results by model dimensionality and experimental design size, we identify combinations of methods that are most promising for specific classes of problems.