Dynamic allocation of participants to treatments in a clinical trial has been an alternative to randomization for nearly 35 years. Design-adaptive allocation is a particularly flexible kind of dynamic allocation. Every investigation of dynamic allocation methods has shown that they improve balance of prognostic factors across treatment groups, but there have been lingering doubts about their influence on the validity of statistical inferences. Here we report the results of a simulation study focused on this and similar issues. Overall, it is found that there are no statistical reasons, in the situations studied, to prefer randomization to design-adaptive allocation. Specifically, there is no evidence of bias, the number of participants wasted by randomization in small studies is not trivial, and when the aim is to place bounds on the prediction of population benefits, randomization is quite substantially less efficient than design-adaptive allocation. A new, adjusted permutation estimate of the standard deviation of the regression estimator under design-adaptive allocation is shown to be an unbiased estimate of the true sampling standard deviation, resolving a long-standing problem with dynamic allocations. These results are shown in situations with varying numbers of balancing factors, different treatment and covariate effects, different covariate distributions, and in the presence of a small number of outliers.