Tone curves are a key feature in any image processing pipeline, and are used to change the pixel values of an input image to find an output image that looks better. Perhaps the most widely deployed tone curve algorithm is Contrast Limited Histogram Equalisation (CLHE). CLHE is an iterative algorithm that tone maps an input image so that the histogram of the output is (approximately) maximally uniform subject to the constraint that the tone curve has bounded slope (neither too large or too small).In this paper, we build upon a neural network framework [1] that was recently developed to deliver CLHE in fewer iterations (each layer in the neural network is analogous to a single iteration of CLHE, but the network has fewer layers than the number of iterations needed by CLHE). The key contribution of this paper is to show that the same network architecture can be used to implement a more complex (and more powerful) tone mapping algorithm. Experiments validate our method.