Pure rotational spectra of rare isotopomers of sulfur monoxide, SO, have been recorded with the Cologne Terahertz Spectrometer, Germany, and the millimeter- and submillimeter-wave spectrometer at Nobeyama, Japan. In total, 176 new transitions have been measured in the X3Sigma- electronic ground state, including the first laboratory detection of the rare isotopomer 36SO. New lines are also reported for 33SO and S17O in their vibrational ground states, and for 33SO and S18O in the first excited vibrational state. A simultaneous fit of 451 transitions has led to an improved set of isotopically invariant parameters for rotation and fine structure. Hyperfine structure constants for 33SO and S17O have been obtained also from the global fit, including first values for the magnetic nuclear spin-rotation interaction. These are compared to other molecules. The isotopically invariant parameters allow precise frequency predictions for the submillimeter-wave region far beyond 1 THz for all SO isotopomers, of importance to astrophysical applica- tions.