Randomized clinical trials adhere more closely to pre-agreed-on protocols than almost any other type of experiment, yet we can tighten up their analysis if we desire. If we convert the analysis into a randomization analysis--where the one set of data is analyzed many times--once as though each acceptable assignment has been employed, we can eliminate any dependence of the analysis on statistical or probabilistic assumptions. To do this effectively when many assignments could be acceptable, we can go to double randomization, in which a subset, usefully kept balanced, of acceptable assignments is selected (perhaps randomly) before data acquisition. If we have one covariate, adjustment for which answers a question that is at least as appropriate, we can easily build on this. Imperfect covariance adjustments can help almost as much as perfect ones. If it is appropriate to work with many covariate(s), it is often desirable to first construct a (few) compound covariate(s) and then work with it (them). Often we can base the coefficients in our compound covariate on the univariate regressions of response on single covariates. Doing this within each arm of the trial and pooling keeps the fitting of the final adjustment unbiased. Since we can prespecify how the compounds are to be calculated and fitted, we can do all this while retaining rigid prespecification. Prespecification, randomization, and intelligent use of covariates combined to make the resulting significance analysis of platinum standard quality. (If we want confidence statements, as we ordinarily should, it may make sense, for technical reasons, to plan for somewhat less than platinum standard quality).