Ordered subsets expectation maximization (OS-EM) is widely used to accelerate image reconstruction in single photon emission computed tomography (SPECT). Speedup of OS-EM over maximum likelihood expectation maximization (ML-EM) is close to the number of subsets used. Although a high number of subsets can shorten reconstruction times significantly, it can also cause severe image artifacts such as improper erasure of reconstructed activity if projections contain few counts. We recently showed that such artifacts can be prevented by using a count-regulated OS-EM (CR-OS-EM) algorithm which automatically adapts the number of subsets for each voxel based on the estimated number of counts that the voxel contributed to the projections. While CR-OS-EM reached high speed-up over ML-EM in high-activity regions of images, speed in low-activity regions could still be very slow. In this work we propose similarity-regulated OS-EM (SR-OS-EM) as a much faster alternative to CR-OS-EM. SR-OS-EM also automatically and locally adapts the number of subsets, but it uses a different criterion for subset regulation: the number of subsets that is used for updating an individual voxel depends on how similar the reconstruction algorithm would update the estimated activity in that voxel with different subsets. Reconstructions of an image quality phantom and in vivo scans show that SR-OS-EM retains all of the favorable properties of CR-OS-EM, while reconstruction speed can be up to an order of magnitude higher in low-activity regions. Moreover our results suggest that SR-OS-EM can be operated with identical reconstruction parameters (including the number of iterations) for a wide range of count levels, which can be an additional advantage from a user perspective since users would only have to post-filter an image to present it at an appropriate noise level.