Dose-finding studies are often performed to identify the dose corresponding to a particular effectiveness. In anesthesiology, the up-and-down or biased coin design (BCD) has become the most popular design, based on its simple implementation and minimal parametric assumptions. Several articles in that field claim the BCD outperforms other methods even though such claims are not supported with empirical evidence. To assess the accuracy of these claims, we compared the BCD to the continual reassessment method (CRM) using a simulation study. The form of the dose-response curve, sample size, target effective dose, and starting dose were varied to determine the impact of these factors on the relative effectiveness of each method. Several methods for dose-estimation using the BCD, the mean, truncated mean, and isotonic regression, are compared to the CRM using correctly and incorrectly specified dose-response curves. We provide scenarios where the performance of the BCD is comparable to that of the CRM as demonstrate conditions where the CRM outperforms the BCD.