Network compression techniques that combine tensor decompositions and pruning have shown promise in leveraging the advantages of both strategies. In this work, we propose enhanced Network cOmpRession through TensOr decompositions and pruNing (NORTON), a novel method for network compression. NORTON introduces the concept of filter decomposition, enabling a more detailed decomposition of the network while preserving the weight's multidimensional properties. Our method incorporates a novel structured pruning approach, effectively integrating the decomposed model. Through extensive experiments on various architectures, benchmark datasets, and representative vision tasks, we demonstrate the usefulness of our method. NORTON achieves superior results compared to state-of-the-art (SOTA) techniques in terms of complexity and accuracy. Our code is also available for research purposes.