Complete case analyses of complete crossover designs provide an opportunity to make comparisons based on patients who can tolerate all treatments. It is argued that this provides a means of estimating a principal stratum strategy estimand, something which is difficult to do in parallel group trials. While some trial users will consider this a relevant aim, others may be interested in hypothetical strategy estimands, that is, the effect that would be found if all patients completed the trial. Whether these estimands differ importantly is a question of interest to the different users of the trial results. This paper derives the difference between principal stratum strategy and hypothetical strategy estimands, where the former is estimated by a complete-case analysis of the crossover design, and a model for the dropout process is assumed. Complete crossover designs, that is, those where all treatments appear in all sequences, and which compare t treatments over p periods with respect to a continuous outcome are considered. Numerical results are presented for Williams designs with four and six periods. Results from a trial of obstructive sleep apnoea-hypopnoea (TOMADO) are also used for illustration. The results demonstrate that the percentage difference between the estimands is modest, exceeding 5% only when the trial has been severely affected by dropouts or if the within-subject correlation is low.