Network pruning is widely used to compress Deep Neural Networks (DNNs). The Soft Filter Pruning (SFP) method zeroizes the pruned filters during training while updating them in the next training epoch. Thus the trained information of the pruned filters is completely dropped. To utilize the trained pruned filters, we proposed a SofteR Filter Pruning (SRFP) method and its variant, Asymptotic SofteR Filter Pruning (ASRFP), simply decaying the pruned weights with a monotonic decreasing parameter. Our methods perform well across various netowrks, datasets and pruning rates, also transferable to weight pruning. On ILSVRC-2012, ASRFP prunes 40% of the parameters on ResNet-34 with 1.63% top-1 and 0.68% top-5 accuracy improvement. In theory, SRFP and ASRFP are an incremental regularization of the pruned filters. Besides, We note that SRFP and ASRFP pursue better results while slowing down the speed of convergence.