In this work, we tackle the task of estimating the 6D pose of an object from point cloud data. While recent learning-based approaches have shown remarkable success on synthetic datasets, we have observed them to fail in the presence of real-world data. We investigate the root causes of these failures and identify two main challenges: The sensitivity of the widely-used SVD-based loss function to the range of rotation between the two point clouds, and the difference in feature distributions between the source and target point clouds. We address the first challenge by introducing a directly supervised loss function that does not utilize the SVD operation. To tackle the second, we introduce a new normalization strategy, Match Normalization. Our two contributions are general and can be applied to many existing learning-based 3D object registration frameworks, which we illustrate by implementing them in two of them, DCP and IDAM. Our experiments on the real-scene TUD-L Hodan et al. 2018, LINEMOD Hinterstoisser et al. 2012 and Occluded-LINEMOD Brachmann et al. 2014 datasets evidence the benefits of our strategies. They allow for the first-time learning-based 3D object registration methods to achieve meaningful results on real-world data. We therefore expect them to be key to the future developments of point cloud registration methods.