Deploying deep convolutional neural networks on Internet-of-Things (IoT) devices is challenging due to the limited computational resources, such as limited SRAM memory and Flash storage. Previous works re-design a small network for IoT devices, and then compress the network size by mixed-precision quantization. This two-stage procedure cannot optimize the architecture and the corresponding quantization jointly, leading to sub-optimal tiny deep models. In this work, we propose a one-stage solution that optimizes both jointly and automatically. The key idea of our approach is to cast the joint architecture design and quantization as an Entropy Maximization process. Particularly, our algorithm automatically designs a tiny deep model such that: 1) Its representation capacity measured by entropy is maximized under the given computational budget; 2) Each layer is assigned with a proper quantization precision; 3) The overall design loop can be done on CPU, and no GPU is required. More impressively, our method can directly search high-expressiveness architecture for IoT devices within less than half a CPU hour. Extensive experiments on three widely adopted benchmarks, ImageNet, VWW and WIDER FACE, demonstrate that our method can achieve the state-of-the-art performance in the tiny deep model regime. Code and pre-trained models are available at https://github.com/alibaba/lightweight-neural-architecture-search.