Under the framework of Bayesian model selection, we propose a nonparametric overdose control (NOC) design for dose finding in phase I clinical trials. Each dose assignment is guided via a feasibility bound, which thereby can control the number of patients allocated to excessively toxic dose levels. We further develop a fractional NOC (fNOC) design in conjunction with a so-called fractional imputation approach, to account for late-onset toxicity outcomes. Extensive simulation studies have been conducted to show that both the NOC and fNOC designs have robust and satisfactory finite-sample performance compared with the existing dose finding designs. The proposed methods also possess several desirable properties: treating patients more safely and also neutralizing the aggressive escalation to overly toxic doses when the toxicity outcomes are late-onset. We also generalize the NOC design to handle drug-combination trials and phase I/II trials.