Recently, Wong et al. [29] showed that adversarial training with single-step FGSM leads to a characteristic failure mode named catastrophic overfitting (CO), in which a model becomes suddenly vulnerable to multi-step attacks. They showed that adding a random perturbation prior to FGSM(RS-FGSM) seemed to be sufficient to prevent CO. However, Andriushchenko and Flammarion [1] observed that RS-FGSM still leads to CO for larger perturbations, and proposed an expensive regularizer (GradAlign) to avoidCO. In this work, we methodically revisit the role of noise and clipping in single-step adversarial training. Contrary to previous intuitions, we find that using a stronger noise around the clean sample combined with not clipping is highly effective in avoiding CO for large perturbation radii. Based on these observations, we then propose Noise-FGSM(N-FGSM) that, while providing the benefits of single-step adversarial training, does not suffer from CO. Empirical analyses on a large suite of experiments show that N-FGSM is able to match or surpass the performance of previous single-step methods while achieving a 3× speed-up.