Obtaining large-scale noisy/clean image pairs from the real world to train a denoising model is a difficult and cumbersome task. Self-supervised image denoisers have gained recent attention by adopting blind-spot networks to remove noise from single noisy images. However, the results of blind-spot denoisers suffer from losses of image detail caused by the selection of random masks. Here, we propose an edge-enhanced denoising approach called Self2Grad that compensates for the loss of important details when using self-supervised networks. Specifically, we develop a gradient-regularized loss function, which when added to the overall network loss acts to preserve details in images processed by blind-spot networks. In addition, we show that the loss obtained with Self2Grad is approximately equal to the loss incurred by supervised approaches. When compared to state-of-the-art (SOTA) blind-spot denoisers, Self2Grad delivers superior performance on both synthetic and real-world datasets. Indeed, Self2Grad attains comparable denoising results as methods that operate on multiple images. In particular, Self2Grad is especially effective on images corrupted by high levels of noise.