We present III-Sb resonant cavity-enhanced (RCE) photodetectors suitable for gas detection in the mid-wave infrared. AlAsSb/GaSb DBRs and absorbers of bulk InAsSb or a type-II InAsSb-InAs SLS were grown on GaSb, allowing for operation at 3.72 μm or 4.52 μm, with linewidth Δλ < 50 nm and Δλ < 70 nm, respectively. A barrier diode structure was used, and the absorber thickness was limited to 96 nm for InAsSb – or 192 nm for the SLS – in order to limit the dark currents. High quantum efficiency was obtained through the resonant optical field, while the remainder of the cavity was grown using wide-gap AlAsSb spacer layers not contributing to the dark current. By carefully compensation doping the AlAsSb layers, the 3.72 μm device was bandgap-engineered for a flat Fermi level in the thin absorber, and hence dark currents which scale with the absorber thickness. This can equate to a >20x reduction in noise compared with a conventional nBn detector with full thickness absorber. At 3.72 μm, performance above the BLIP limit imposed on broadband photodetectors was found by calculating for the specific detectivity.