Perfect blazing with echelle gratings in a high-order Littrow mount exists not only with TM polarization, as can perhaps be assumed, but also with TE and TM polarizations simultaneously. This finding contradicts with a heuristic explanation as to why perfect blazing is not possible simultaneously in TE and TM polarizations given by Loewen and Popov [Diffraction Gratings and Applications (Marcel Dekker, 1997)]. As a matter of fact, in the ideal case of infinite conductivity, light is diffracted in the Littrow order with 100% efficiency for both polarization states. For metal gratings, a small loss occurs. Three conditions are necessary for perfect blazing: (A) the apex angle must be very close to 90°, (B) a specific Littrow order has to be used, and (C) the blaze angle has to be 4° to 6° larger than the Littrow angle. The last property is particularly intriguing because typically the difference between the two angles is smaller than 1.0°.