  For the Burgers equation, the entropy solution becomes instantly BV with only
$L^\infty$ initial data. For conservation laws with genuinely nonlinear
discontinuous flux, it is well known that the BV regularity of entropy
solutions is lost. Recently, this regularity has been proved to be fractional
with s = 1/2. Moreover, for less nonlinear flux the solution has still a
fractional regularity 0 < s \leq 1/2. The resulting general rule is the
regularity of entropy solutions for a discontinuous flux is less than for a
smooth flux. In this paper, an optimal geometric condition on the discontinuous
flux is used to recover the same regularity as for the smooth flux with the
same kind of nonlinearity.
