Frequency-selective bolometers (FSBs) are a new type of detector for millimeter and submillimeter wavelengths that are transparent to all but a narrow range of frequencies as set by characteristics of the absorber itself. Therefore stacks of FSBs tuned to different frequencies provide a low-loss compact method for utilizing a large fraction of the light collected by a telescope. Tests of prototype FSBs indicate that the absorption spectra are well predicted by models, that peak absolute absorption efficiencies of the order of 50% are attainable, and that their out-of-band transmission is high.