In maximum-likelihood expectation-maximization (MLEM) reconstruction of SPECT images, if both attenuation correction (AC) and detector response correction (DRC) are included, the reconstruction can be too time consuming to be clinically useful. With use of the ordered-subset expectation-maximization (OSEM) reconstruction, it has been reported that the reconstruction time can be substantially reduced. We investigated the reconstruction of point sources in a non-uniform attenuation medium in terms of the normalized FWHM of these sources. We compared MLEM versus OSEM reconstructions; circular versus elliptical orbits; and the presence versus the absence of background activity in the object. We found: (i) that OSEM does speed up the reconstruction by a factor of 10 over MLEM; (ii) that the resolution recovery does not depend on the type of orbit if both AC and DRC are included in the reconstruction; however, when there is background activity, a significant number of iterations are required to alleviate the effect of orbit; (iii) that background activity significantly slows down the resolution recovery of the point sources; and (iv) that if reconstruction only includes AC, and not DRC, changing orbit can change isotropy of recovered resolution, whereas introducing background activity may degrade the recovered resolution and also changes the isotropy.