Molecular beam epitaxy has been used to prepare multilayer structures of CdTe/InSb on (001) InSb at a growth temperature of 300-degrees-C. Transmission electron microscopy and double crystal x-ray diffraction were employed to analyze the multilayer specimens and also a series of single CdTe layers grown on (001) InSb at substrate temperatures ranging from 180 to 300-degrees-C. The detrimental effect on the CdTe layers of increasing the substrate temperature is clearly demonstrated and modification of the Cd:Te flux ratio during growth is shown to reestablish high structural quality material. Both x-ray and transmission electron microscopy studies confirm the high structural quality that can be achieved when multilayers are grown at 300-degrees-C using the modified Cd:Te flux ratio conditions. These analytical techniques also reveal the presence of strain at each CdTe/InSb interface possibly associated with the formation of a thin (less-than-or-equal-to 2 nm) layer of an indium telluride (e.g., In2 Te3). The growth of high structural quality multilayers with individual layer thicknesses less-than-or-equal-to 22.5 nm is seen to break down rapidly as growth proceeds and a possible explanation for this observation is discussed.