We propose a Quantization Guided Training (QGT) method to guide DNN training towards optimized low-bit-precision targets and reach extreme compression levels below 8-bit precision. Unlike standard quantization-aware training (QAT) approaches, QGT uses customized regularization to encourage weight values towards a distribution that maximizes accuracy while reducing quantization errors. One of the main benefits of this approach is the ability to identify compression bottlenecks. We validate QGT using state-of-the-art model architectures on vision datasets. We also demonstrate the effectiveness of QGT with an 81KB tiny model for person detection down to 2-bit precision (representing 17.7x size reduction), while maintaining an accuracy drop of only 3% compared to a floating-point baseline.