The crossover design compares treatments A and B over two periods using sequences AB and BA (the AB|BA design) and is the classic design most often illustrated and critiqued in textbooks. Other crossover designs have been used but their use is relatively rare and not always well understood. This article introduces alternatives to a randomized two-treatment, two-period crossover study design. One strategy, which is to extend the classic AB|BA by adding a third period to repeat one of the two treatments, has several attractive advantages; an added treatment period may not imply a large additional cost but will allow carryover effects to be estimated and compared with the within-subject variability. Careful choice of treatment sequences will enable the first two trial periods to constitute a conventional two-period crossover trial if the third treatment period leads to excessive subject drop-outs. Four alternative designs that address the first-order carryover effect are presented. These designs have more statistical power than the classic design and allow the treatment effects to be estimated, even in the presence of a carryover effect.