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Deep Neural Networks have memory and computational demands that often render them difficult to use in low-resource environments. Also, highly dense networks are over-parameterized and thus prone to overfitting. To address these problems, we introduce a novel algorithm that prunes (sparsifies) weights from the network by taking into account their magnitudes and gradients taken against a validation dataset. Unlike existing pruning methods, our method does not require the network model to be retrained once initial training is completed. On the CIFAR-10 dataset, our method reduced the number of paramters of MobileNet by a factor of 9X, from 14 million to 1.5 million, with just a 3.8% drop in accuracy.