In a cluster randomized cross-over trial, all participating clusters receive both intervention and control treatments consecutively, in separate time periods. Patients recruited by each cluster within the same time period receive the same intervention, and randomization determines order of treatment within a cluster. Such a design has been used on a number of occasions. For analysis of the trial data, the approach of analysing cluster-level summary measures is appealing on the grounds of simplicity, while hierarchical modelling allows for the correlation of patients within periods within clusters and offers flexibility in the model assumptions. We consider several cluster-level approaches and hierarchical models and make comparison in terms of empirical precision, coverage, and practical considerations. The motivation for a cluster randomized trial to employ cross-over of trial arms is particularly strong when the number of clusters available is small, so we examine performance of the methods under small, medium and large (6, 18, 30) numbers of clusters. One hierarchical model and two cluster-level methods were found to perform consistently well across the designs considered. These three methods are efficient, provide appropriate standard errors and coverage, and continue to perform well when incorporating adjustment for an individual-level covariate. We conclude that choice between hierarchical models and cluster-level methods should be influenced by the extent of complexity in the planned analysis.