  The gravitational waves emitted by neutron stars carry unique information
about their structure and composition. Direct detection of these gravitational
waves, however, is a formidable technical challenge. In a recent study we
quantified the hurdles facing searches for gravitational waves from the known
accreting neutron stars, given the level of uncertainty that exists regarding
spin and orbital parameters. In this paper we reflect on our conclusions, and
issue an open challenge to the theoretical community to consider how searches
should be designed to yield the most astrophysically interesting upper limits.
With this in mind we examine some more optimistic emission scenarios involving
spin-down, and show that there are technically feasible searches, particularly
for the accreting millisecond pulsars, that might place meaningful constraints
on torque mechanisms. We finish with a brief discussion of prospects for
indirect detection.
