A number of novel phase I trial designs have been proposed that aim to combine the simplicity of algorithm-based designs with the superior performance of model-based designs, including the modified toxicity probability interval, Bayesian optimal interval, and Keyboard designs. In this article, we review these "model-assisted" designs, contrast their statistical foundations and pros and cons, and compare their operating characteristics with the continual reassessment method. To provide unbiased and reliable results, our comparison is based on 10 000 dose-toxicity scenarios randomly generated using the pseudo-uniform algorithm recently proposed in the literature. The results showed that the continual reassessment method, Bayesian optimal interval, and Keyboard designs provide comparable, superior operating characteristics, and each outperforms the modified toxicity probability interval design. These designs are more likely to correctly select the maximum tolerated dose and less likely to overdose patients.