When applying machine learning to sensitive data, one has to balance between accuracy, information leakage, and computational-complexity. Recent studies combined Homomorphic Encryption with neural networks to make inferences while protecting against information leakage. However, these methods are limited by the width and depth of neural networks that can be used (and hence the accuracy) and exhibit high latency even for relatively simple networks. In this study we provide two solutions that address these limitations. In the first solution, we present more than 10x improvement in latency and enable inference on wider networks compared to prior attempts with the same level of security. The improved performance is achieved by novel methods to represent the data during the computation. In the second solution, we apply the method of transfer learning to provide private inference services using deep networks with latency lower than 0.2 seconds. We demonstrate the efficacy of our methods on several computer vision tasks.