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It has been demonstrated in various contexts that monotonicity leads to better explainability in neural networks. However, not every function can be well approximated by a monotone neural network.We demonstrate that monotonicity can still be used in two ways to boost explainability. First, we use an adaptation of the decomposition of a trained ReLU network into two monotone and convex parts, thereby overcoming numerical obstacles from an inherent blowup of the weights in this procedure. Our proposed saliency methods -- SplitCAM and SplitLRP --improve onstate of the art results on both VGG16 and Resnet18 networks on ImageNet-S across all Quantus saliency metric categories.Second, we exhibit that training a model as the difference between two monotone neural networks results in a system with strong self-explainability properties.