Compressive Raman is a recent framework that allows for large data compression of microspectroscopy during its measurement. Because of its inherent multiplexing architecture, it has shown imaging speeds considerably higher than conventional Raman microspectroscopy. Nevertheless, the low signal-to-noise (SNR) of Raman scattering still poses challenges for high-sensitivity bio-imaging exploiting compressive Raman: (i) the idle solvent acts as a background noise upon imaging small biological organelles, (ii) current compressive spectrometers are lossy precluding high-sensitivity imaging. We present inexpensive high-throughput spectrometer layouts for high-sensitivity compressive hyperspectroscopy. We exploit various modalities of compressive Raman allowing for up to 80X reduction of data storage and 2X microspectroscopy speed up at a 230-nm spatial resolution. Such achievements allowed us to chemically image sub-diffraction-limited biological specimens (lipid bilayers) in few seconds.