Attenuation of photon flux on trajectories between the source and pinhole apertures affects the quantitative accuracy of reconstructed single-photon emission computed tomography (SPECT) images. We propose a Chang-based non-uniform attenuation correction (NUA-CT) for small-animal SPECT/CT with focusing pinhole collimation, and compare the quantitative accuracy with uniform Chang correction based on (i) body outlines extracted from x-ray CT (UA-CT) and (ii) on hand drawn body contours on the images obtained with three integrated optical cameras (UA-BC). Measurements in phantoms and rats containing known activities of isotopes were conducted for evaluation. In (125)I, (201)Tl, (99m)Tc and (111)In phantom experiments, average relative errors comparing to the gold standards measured in a dose calibrator were reduced to 5.5%, 6.8%, 4.9% and 2.8%, respectively, with NUA-CT. In animal studies, these errors were 2.1%, 3.3%, 2.0% and 2.0%, respectively. Differences in accuracy on average between results of NUA-CT, UA-CT and UA-BC were less than 2.3% in phantom studies and 3.1% in animal studies except for (125)I (3.6% and 5.1%, respectively). All methods tested provide reasonable attenuation correction and result in high quantitative accuracy. NUA-CT shows superior accuracy except for (125)I, where other factors may have more impact on the quantitative accuracy than the selected attenuation correction.