Under either the random patient-effect model with sequence effects or the fixed patient-effect model, the usual two-period, two-treatment crossover design, AB,BA, cannot be used to estimate the contrast between direct treatment effects when unequal carryover effects are present. If baseline observations are available, the design AB,BA can validly be used to estimate a treatment contrast. However, the design AB,BA,AA,BB with baseline observations is more efficient. In fact, we show that this design is optimal whether or not baseline observations are available. For experiments with more than two periods, universally optimal designs are found for both models, with and without carryover effects. It is shown that uncertainty about the presence of carryover effects is of little or no consequence, and the addition of baseline observations is of little or no added value for designs with three or more periods; however, if the experiment is limited to only two periods the investigator pays a heavy penalty.