  We investigate the improvement in sensitivity to astrophysical point sources
of energetic ($\gtrsim1$ GeV) neutrinos which can be achieved with angular
and/or energy resolution of the neutrino-induced muon. As a specific example we
consider WIMP annihilation in the Sun and in the Earth as a neutrino source.
The sensitivity is improved by using the angular and energy distribution to
reduce the atmospheric-neutrino background. Although the specific improvements
depend on the backgrounds and assumed sources, the sensitivity to a WIMP signal
may be improved, with equal exposure, by up to roughly a factor of two with
good angular resolution, and by up to roughly a factor of three with good
energy resolution. In case of a positive detection, energy resolution would
also improve the measurement of the neutrino energy spectrum and therefore
provide information on the WIMP mass and composition.
