Abstract: Both transduction and rejection have emerged as important techniques for defending against adversarial perturbations. A recent work by Goldwasser et. al showed that rejection combined with transduction can give *provable* guarantees (for certain problems) that cannot be achieved otherwise. Nevertheless, under recent strong adversarial attacks (GMSA), Goldwasser et al.'s work was shown to have low performance in a practical deep-learning setting. In this paper, we take a step towards realizing the promise of transduction+rejection in more realistic scenarios. Our key observation is that a novel application of a reduction technique by Tramèr, which was until now only used to demonstrate the vulnerability of certain defenses, can be used to actually construct effective defenses. Theoretically, we show that a careful application of this technique in the transductive setting can give significantly improved sample-complexity for robust generalization. Our theory guides us to design a new transductive algorithm for learning a selective model; extensive experiments using state of the art attacks (AutoAttack, GMSA) show that our approach provides significantly better robust accuracy (81.6\% on CIFAR-10 and 57.9\% on CIFAR-100 under $l_\infty$ with budget 8/255) than existing techniques.