The application of deep learning to 3D point clouds is challenging due to its lack of order. Inspired by the point embeddings of PointNet and the edge embeddings of DGCNNs, we propose three improvements to the task of point cloud analysis. First, we introduce a novel feature-attentive neural network layer, a FAT layer, that combines both global point-based features and local edge-based features in order to generate better embeddings. Second, we find that applying the same attention mechanism across two different forms of feature map aggregation, max pooling and average pooling, gives better performance than either alone. Third, we observe that residual feature reuse in this setting propagates information more effectively between the layers, and makes the network easier to train. Our architecture achieves state-of-the-art results on the task of point cloud classification, as demonstrated on the ModelNet40 dataset, and an extremely competitive performance on the ShapeNet part segmentation challenge.