The stepped wedge design is an appealing longitudinal cluster randomised trial design. However, it places a large burden on participating clusters by requiring all clusters to collect data in all periods of the trial. The staircase design may be a desirable alternative: treatment sequences consist of a limited number of measurement periods before and after the implementation of the intervention. In this article, we explore the relative efficiency of the stepped wedge design to several variants of the 'basic staircase' design, which has one control followed by one intervention period in each sequence. We model outcomes using linear mixed models and consider a sampling scheme where each participant is measured once. We first consider a basic staircase design embedded within the stepped wedge design, then basic staircase designs with either more clusters or larger cluster-period sizes, with the same total number of participants and with fewer total participants than the stepped wedge design. The relative efficiency of the designs depends on the intracluster correlation structure, correlation parameters and the trial configuration, including the number of sequences and cluster-period size. For a wide range of realistic trial settings, a basic staircase design will deliver greater statistical power than a stepped wedge design with the same number of participants, and in some cases, with even fewer total participants.