  We obtain new results about the high-energy distribution of resonances for
the one-dimensional Schr\"odinger operator. Our primary result is an upper
bound on the density of resonances above any logarithmic curve in terms of the
singular support of the potential. We also prove results about the distribution
of resonances in sectors away from the real axis, and construct a class of
potentials producing multiple sequences of resonances along distinct
logarithmic curves, explicitly calculating the asymptotic location of these
resonances. The results are unified by the use of an integral representation of
the reflection coefficients.
