Learned image compression methods generally optimize a rate-distortion loss, trading off improvements in visual distortion for added bitrate. Increasingly, however, compressed imagery is used as an input to deep learning networks for various tasks such as classification, object detection, and super-resolution. We propose a recognition-aware learned compression method, which optimizes a rate-distortion loss alongside a task-specific loss, jointly learning compression and recognition networks. We augment a hierarchical autoencoder-based compression network with an EfficientNet recognition model and use two hyperparameters to trade off between distortion, bitrate, and recognition performance. We characterize the classification accuracy of our proposed method as a function of bitrate and find that for low bitrates our method achieves as much as 26% higher recognition accuracy at equivalent bitrates compared to traditional methods such as Better Portable Graphics (BPG).