Abstract Compressive speech enhancement (CSE) has gained popularity in recent years as it bypasses the need for noise estimation. Parallel to that, modulation domain has been widely studied in speech applications as it offers a more compact representation and is closely associated with speech intelligibility enhancement. Motivated by the development in modulation domain and CSE, this paper seeks to explore the suitability of modulation domain based sparse reconstruction for use in CSE. The main idea is to study if the increased sparsity in the modulation domain would benefit sparse reconstruction in CSE. The findings reveal that modulation transformation is sparser and offers a stronger restricted isometry property (RIP) compared to the frequency transformation, which is essential for sparse recovery with a high probability. The results are then extended to show that the sparse reconstruction error in the modulation domain is upper bounded by the frequency domain. Experimental results in a CSE setting concur with the theoretical derivations, with modulation domain CSE outperforming the frequency domain CSE through different speech quality measures.