The refractive index of a highly-doped semiconductor layer has long been known to decrease substantially in the mid-infrared as a result of free-carrier effects, most notably in plasmon-enhanced waveguides used for quantum cascade lasers. Here, we explore plasmon-enhanced distributed Bragg reflectors for use in the mid-infrared that exploit the same free-carrier driven reduction in refractive index. The performance of such structures is simulated over a range of achievable doping densities and design wavelengths in order to examine the competing effects of increased refractive index contrast and free-carrier losses. We demonstrate a 5-pair plasmon-enhanced distributed Bragg reflector with a 4.2 μm design wavelength exhibiting equal reflectance to a lossless, 9-pair AlAsSb/GaSb distributed Bragg reflector while being 43 % less thick.