Accurate spectral data of HS32OH and HS34OH at 1.3 THz were recorded using a synthesizer based multiplier spectrometer. The spectra were analyzed together with data from an earlier study which contain measurements at 1.9 THz. The combination of both data sets allows to determine experimentally the tunneling splitting of energy levels with Ka=4 and 5 for the first time. The obtained results are essential to test a novel model on torsional tunneling splitting in HSOH. Transitions with Ka=10, Ka=21, and Ka=32 all exhibit strong c-type and somewhat weaker b-type transitions. In contrary, transitions with Ka=43 display only c-type but no b-type transitions. The absence of b-type transitions is completely unexpected and yet not well understood. For the HS34OH isotopolog the data set has been substantially extended by the new measurements of Qr3-branch transitions at 1.3 THz. Based on the new data the accuracy of the HS34OH molecular parameters has been significantly improved.

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