The success of large BERT models has raised the demand for model compression methods to reduce model size and computational cost. Quantization can reduce the model size and inference latency, making inference more efficient, without changing its stucture, but it comes at the cost of performance degradation. Due to the complex loss landscape of ternarized/binarized BERT, we present an efficient two-stage progressive quantization method in which we fine tune the model with quantized weights and progressively lower its bits, and then we fine tune the model with quantized weights and activations. At the same time, we strategically choose which bitwidth to fine-tune on and to initialize from, and which bitwidth to fine-tune under augmented data to outperform the existing BERT binarization methods without adding an extra module, compressing the binary model 18% more than previous binarization methods or compressing BERT by 31x w.r.t. to the full-precision model. Our method without data augmentation can outperform existing BERT ternarization methods.