  We study various aspects of power suppressed as well as exponentially
suppressed corrections in the asymptotic expansion of the degeneracy of quarter
BPS dyons in N=4 supersymmetric string theories. In particular we explicitly
calculate the power suppressed corrections up to second order and the first
exponentially suppressed corrections. We also propose a macroscopic origin of
the exponentially suppressed corrections using the quantum entropy function
formalism. This suggests a universal pattern of exponentially suppressed
corrections to all four dimensional extremal black hole entropies in string
theory.
