Automatically determining three-dimensional human pose from monocular RGB image data is a challenging problem. The two-dimensional nature of the input results in intrinsic ambiguities which make inferring depth particularly difficult. Recently, researchers have demonstrated that the flexible statistical modelling capabilities of deep neural networks are sufficient to make such inferences with reasonable accuracy. However, many of these models use coordinate output techniques which are memory-intensive, not differentiable, and/or do not spatially generalise well. We propose improvements to 3D coordinate prediction which avoid the aforementioned undesirable traits by predicting 2D marginal heatmaps under an augmented soft-argmax scheme. Our resulting model, MargiPose, produces visually coherent heatmaps whilst maintaining differentiability. We are also able to achieve state-of-the-art accuracy on publicly available 3D human pose estimation data.