We have completed extensive synchrotron reflectivity measurements on several iridium mirrors which were intentionally coated with thin layers (100 angstroms or less) of polyethylene, a hydrocarbon contaminant. The purpose was to verify theoretical predictions of alterations in reflection efficiency of an iridium surface for various thicknesses of hydrocarbon contamination, and to evaluate the acceptability of attainable upper limits of such contamination for the mirrors aboard NASA's Advanced X-ray Astrophysics Facility (AXAF). Although the deposition of such thin layers is problematic with no systematic guarantee of uniform thickness or density, successful analysis by modeling the contaminant as a uniform surface layer may be done, within a limited X-ray energy range. The M-edges of iridium are significantly affected by the polyethylene layers. For the most part, contamination increases the reflectance in the M-edge range over that of bare iridium, although cross-over points between contaminated and uncontaminated mirrors occur at several angles relevant to AXAF. However, calibratability of the reflectance is a more significant issue than X-ray mirror efficiency. We present the modeling results for three thicknesses of polyethylene, and discuss the implications for the performance of AXAF mirrors and their calibratability.