The extraction of a haze from the WMAP microwave skymaps is based on subtraction of known foregrounds, viz. free-free (bremsstrahlung), thermal dust and synchrotron, each traced by other skymaps. While the 408 MHz all-sky survey is used for the synchrotron template, the WMAP bands are at tens of GHz where the spatial distribution of the radiating cosmic ray electrons ought to be quite different because of the energy-dependence of their diffusion in the Galaxy. The systematic uncertainty this introduces in the residual skymap is comparable to the claimed haze and can, for certain source distributions, have a very similar spectrum and latitudinal profile and even a somewhat similar morphology. Hence caution must be exercised in interpreting the haze as a physical signature of, e.g., dark matter annihilation in the Galactic centre.