Greedy sparse recovery algorithms are studied in the structured sparsity (sparsity in levels) framework. Recovery guarantees are provided for Normalized Iterative Hard Thresholding and Conjugate Gradient Iterative Hard Thresholding in the form of restricted isometry properties for sparsity in levels. Empirical results indicate that CGIHT is comparable to CoSaMP in recovery capability in the structured setting, while maintaining the computational complexity of NIHT. While exploiting structured sparsity improves recovery performance, pessimistic theoretical guarantees mask when practitioners should use these algorithms; the empirical results offer guidance for using the original greedy algorithms over CGIHT in Levels.