This paper presents a set of full-resolution lossy image compression methods based on neural networks. Each of the architectures we describe can provide variable compression rates during deployment without requiring retraining of the network: each network need only be trained once. All of our architectures consist of a recurrent neural network (RNN)-based encoder and decoder, a binarizer, and a neural network for entropy coding. We compare RNN types (LSTM, associative LSTM) and introduce a new hybrid of GRU and ResNet. We also study "one-shot" versus additive reconstruction architectures and introduce a new scaled-additive framework. We compare to previous work, showing improvements of 4.3%-8.8% AUC (area under the rate-distortion curve), depending on the perceptual metric used. As far as we know, this is the first neural network architecture that is able to outperform JPEG at image compression across most bitrates on the rate-distortion curve on the Kodak dataset images, with and without the aid of entropy coding.