Recently Koch et al. suggested an interesting approach for covariate adjustment in randomized clinical trials. Here we report our experience with the approach in Assent II, a large randomized trial comparing 30-day mortality rates of two thrombolytic treatments. Data from the Gusto-I study and a recent successor to the Assent II study will also be used. Further, we balance the advantage of covariate adjustment (with Koch's method) to the extra efforts and resources necessary. In this context we highlight the fact that there is a potential risk of using a covariate-adjusted analysis as primary analysis and show that covariate adjustment has the least effect when it is needed most. Analytic results will be given to quantify this risk and a simulation study illustrates our findings.