High-redshift, dust-obscured galaxies, selected to be luminous in the radio but relatively faint at 850 μm, appear to represent a different population from the ultraluminous submillimeter-bright population. They may be star-forming galaxies with hotter dust temperatures, or they may have lower far-infrared luminosities and larger contributions from obscured active galactic nuclei (AGNs). Here we present observations of three z～2 examples of this population, which we term "submillimeter-faint radio galaxies" (SFRGs; RG J163655, RG J131236, and RG J123711) in CO(3-2) using the IRAM Plateau de Bure Interferometer to study their gas and dynamical properties. We estimate the molecular gas mass in each of the three SFRGs (8.3×10~9, <5.6×10~9, and 15.4×10~9 M_☉, respectively) and, in the case of RG J163655, a dynamical mass by measurement of the width of the CO(3-2) line (8×10~(10) csc~2i M_☉). While these gas masses are substantial, on average they are 4 times lower than submillimeter-selected galaxies (SMGs). Radio-inferred star formation rates ( = 970 M_☉ yr~(-1)) suggest much higher star formation efficiencies than are found for SMGs and shorter gas depletion timescales (～ 11 Myr), much shorter than the time required to form their current stellar masses (～160 Myr; ～10~(11) M_☉). By contrast, star formation rates (SFRs) may be overestimated by factors of a few, bringing the efficiencies in line with those typically measured for other ultraluminous star-forming galaxies and suggesting that SFRGs are more like ultraviolet-selected (UV-selected) star-forming galaxies with enhanced radio emission. A tentative detection of RG J163655 at 350 μm suggests hotter dust temperatures, and thus gas-to-dust mass fractions, similar to the SMGs.
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