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Weight-only quantization has emerged as a promising solution, significantly reducing memory and storage needs without sacrificing too much performance. In this study, we introduce SignRound, a method that leverages signed gradient descent (SignSGD) to optimize rounding values and weight clipping in just 200 steps. SignRound integrates the advantages of Quantization-Aware Training (QAT) and Post-Training Quantization (PTQ), delivering exceptional results across 2 to 4 bits while minimizing tuning costs and avoiding additional inference overhead. For example, SignRound achieved absolute average accuracy improvements ranging from 6.91% to 33.22% at 2bits, as measured by the average zero-shot accuracy across 11 tasks. It also demonstrates strong generalization in recent models, achieving near-lossless 4-bit quantization in most scenarios. 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