A longstanding problem in astrochemistry is the inability of many current models to account for missing sulfur content. Many relatively simple species that may be good candidates to sequester sulfur have not been measured experimentally at the high spectral resolution necessary to enable radioastronomical identification. On the basis of new laboratory data, we report searches for the rotational lines in the microwave, millimeter, and submillimeter regions of the sulfur-containing hydrocarbon HCCSH. This simple species would appear to be a promising candidate for detection in space owing to the large dipole moment along its b-inertial axis, and because the bimolecular reaction between two highly abundant astronomical fragments (CCH and SH radicals) may be rapid. An inspection of multiple line surveys from the centimeter to the far-infrared toward a range of sources from dark clouds to high-mass star-forming regions, however, resulted in nondetections. An analogous search for the lowest-energy isomer, H2CCS, is presented for comparison, and also resulted in nondetections. Typical upper limits on the abundance of both species relative to hydrogen are 10−9–10−10. We thus conclude that neither isomer is a major reservoir of interstellar sulfur in the range of environments studied. Both species may still be viable candidates for detection in other environments or at higher frequencies, providing laboratory frequencies are available.