  Extended Self-Similarity (ESS), a procedure that remarkably extends the range
of scaling for structure functions in Navier--Stokes turbulence and thus allows
improved determination of intermittency exponents, has never been fully
explained. We show that ESS applies to Burgers turbulence at high Reynolds
numbers and we give the theoretical explanation of the numerically observed
improved scaling at both the infrared and ultraviolet end, in total a gain of
about three quarters of a decade: there is a reduction of subdominant
contributions to scaling when going from the standard structure function
representation to the ESS representation. We conjecture that a similar
situation holds for three-dimensional incompressible turbulence and suggest
ways of capturing subdominant contributions to scaling.
