  By generalizing earlier work of Johnston & Kulkarni, we present a detailed
description of the reduction in the signal-to-noise ratio for observations of
binary pulsars. We present analytical expressions, and provide software, to
calculate the sensitivity reduction for orbits of arbitrary eccentricity. We
find that this reduction can be quite significant, especially in the case of a
massive companion like another neutron star or a black hole. On the other hand,
the reduction is less for highly eccentric orbits. We also demonstrate that
this loss of sensitivity can be recovered by employing "acceleration search" or
"acceleration-jerk search" algorithms.
