  Drag reduction by polymers is bounded between two universal asymptotes, the
von-K\'arm\'an log-law of the law and the Maximum Drag Reduction (MDR)
asymptote. It is theoretically understood why the MDR asymptote is universal,
independent of whether the polymers are flexible or rodlike. The cross-over
behavior from the Newtonian von-K\'arm\'an log-law to the MDR is however not
universal, showing different characteristics for flexible and rodlike polymers.
In this paper we provide a theory for this cross-over phenomenology.
