We propose a new method for fully automatic landmark localisation using Convolutional Neural Networks (CNNs). Training a CNN to estimate a Gaussian response (“heatmap”) around each target point is known to be effective for this task. We show that better results can be obtained by training a CNN to predict the offset to the target point at every location, then using these predictions to vote for the point position. We show the advantages of the approach, including those of using a novel loss function and weighting scheme. We evaluate on a dataset of radiographs of child hips, including both normal and severely diseased cases. We show the effect of varying the training set size. Our results show significant improvements in accuracy and robustness for the proposed method compared to a standard heatmap prediction approach and comparable results with a traditional Random Forest method.