  We prove regularity estimates for entropy solutions to scalar conservation
laws with a force. Based on the kinetic form of a scalar conservation law, a
new decomposition of entropy solutions is introduced, by means of a
decomposition in the velocity variable, adapted to the non-degeneracy
properties of the flux function. This allows a finer control of the degeneracy
behavior of the flux. In addition, this decomposition allows to make use of the
fact that the entropy dissipation measure has locally finite singular moments.
Based on these observations, improved regularity estimates for entropy
solutions to (forced) scalar conservation laws are obtained.
