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Deep Neural Networks (DNN) based single-channel speech enhancement techniques have surpassed traditional techniques in handling non-stationary noise, however, they are computationally demanding. In this work, we introduce a novel Hierarchical Framework for DNNs (HF-DNN) for speech enhancement that replaces a single complex and computationally expensive DNN model with multiple simpler and less complex DNNs that are hierarchically connected. This is achieved by using structured codebooks of speech parameters, like log power spectra, that are generated by exploiting hierarchical relation between the speech training data. The proposed HF-DNN reduces computational complexity significantly compared to a large DNN while maintaining speech enhancement performance. Importantly, such a framework can be extended to other speech processing tasks, such as speech recognition, speaker verification, etc., where parametric models of speech data are utilized.