Patient motion during positron emission tomography scans leads to significant resolution loss and image degradation. Motion-compensated image reconstruction (MCIR) algorithms have proven to be reliable correction methods given accurate deformation fields. However, although ordered subsets (OS) are widely used to speed up the convergence, OS-MCIR algorithms are still computationally expensive. This study concentrates on acceleration of OS-MCIR algorithms through two methods: combining OS with motion subsets and use of an initial estimate based on reference gate data. These approaches were compared to two existing OS-MCIR algorithms and post-reconstruction registration using data from the NCAT phantom. The methods were evaluated in terms of noise, lesion bias and contrast-to-noise ratio (CNR). The straightforward combination of motion subsets with projection subsets (OSGEM) produced inferior results (lower CNR, p < 0.01) to existing OS-MCIR algorithms. The addition of a spacer step using data from all gates to OSGEM resulted in an algorithm (SS-OSGEM) that generated images that were statistically consistent with those from existing OS-MCIR algorithms (no significant difference in CNR, p > 0.05) at one third of the computational expense. The use of a reference gate initial estimate (MCDOi) resulted in comparable image quality in terms of bias and CNR (p > 0.05) at half the computational burden. This study indicates that MCDOi and SS-OSGEM in particular are attractive accelerated OS-MCIR approaches.