Cassini Ion Neutral Mass Spectrometer (INMS) measurements from roughly a hundred Titan encounters over the Cassini mission yield neutral and ion densities systematically lower, by factors approximately 2 to 3, than estimates from several other spacecraft systems, including the Attitude and Articulation Control System, and Navigation system. In this paper we present a new INMS instrument sensitivity model, obtained by re-analyzing (1) the capture and transmission of neutral gas through the instrument, and (2) the detector gain reduction during pre-launch testing. By correcting for an under-estimation of gas leakage out of the instrument into space by the original calibration model, and adjusting for the gain change, the new model brings INMS densities into much closer agreement with the other Cassini systems. Accordingly, the INMS ion densities are revised upward by a constant detector sensitivity correction factor of 1.55 ± 21 %, while the neutral sensitivities have a complex instrument pointing direction dependence, due (mostly) to the effect of the INMS vent and antechamber-to-closed source tube. In the special case of on-ram pointing the neutral densities are revised upward by a constant factor of 2.2 ± 23 %. The corrected neutral and ion sensitivities given here are applicable to all previously published INMS results at Titan, Enceladus and elsewhere in the Saturn system. The new model gives reliable densities at high ram angles, in some cases above 90 degrees, thereby expanding the list of Titan flybys from which INMS densities may be extracted. We apply the model to obtain accurate densities from several off-ram Titan flybys which gave unusual neutral density vs. altitude profiles, or unreasonably high densities, with the original calibration.