McKenna burners are widely used in the combustion community for producing "flat" premixed flames. These flames are considered as standards for the development and calibration of optical techniques. Rich premixed flames produced by McKenna burners are frequently investigated in order to understand soot formation processes both by optical and by sampling techniques. Measurements are normally performed along the axis of the flames, with a uniform distribution of temperature and species concentration assumed in the radial direction. In this work it is shown that the soot radial profiles of rich premixed ethylene-air flames produced by a McKenna burner with a stainless steel porous plug may be far from being "flat." Soot is mainly distributed in an annular region and nonsoot fluorescing species are present in the core of the flames. This surprising result was verified under several working conditions. Furthermore, flames cannot be considered axial-symmetric but present a skewed soot distribution. Another McKenna burner with a bronze porous disk was used to produce flames of the same equivalence ratio and flows. These flames show a completely different soot radial profile, closer to the claimed flat distribution. These results cast doubts about the conclusions drawn in several studies on soot formation performed with a stainless steel McKenna burner.