We introduce Softmax Gradient Tampering, a technique for modifying the gradients in the backward pass of neural networks in order to enhance their accuracy. Our approach transforms the predicted probability values using a power-based probability transformation and then recomputes the gradients in the backward pass. This modification results in a smoother gradient profile, which we demonstrate empirically and theoretically. We do a grid search for the transform parameters on residual networks. We demonstrate that modifying the softmax gradients in ConvNets may result in increased training accuracy, thus increasing the fit across the training data and maximally utilizing the learning capacity of neural networks. We get better test metrics and lower generalization gaps when combined with regularization techniques such as label smoothing. Softmax gradient tampering improves ResNet-50's test accuracy by $0.52\%$ over the baseline on the ImageNet dataset. Our approach is very generic and may be used across a wide range of different network architectures and datasets.