In the spatially conformally flat (IWM) approach to initial data, data sets
for neutron-star binaries are constructed by solving a set of five field
equations, the initial value equations and the spatial trace of the Einstein
equation, for five potentials.  Because there are six independent metric
components, one degree of freedom is unspecified, and the resulting data
sets do not have circular orbits.  Recent work centers on two ways to include
the remaining, degree of freedom.  In the waveless approximation, one solves
the full set of field equations for the full metric, but terms involving
second time derivatives of the metric are discarded. Where IWM data sets are
accurate only to 1PN (first post-Newtonian) order, the waveless approximation
is accurate to 2 PN order (and can be made accurate to 3PN order, ignoring the
radiative 2 1/2 PN contribution).  A convergent code has been constructed and
used for recent binary simulations.  In a helically symmetric approach, the
full set of exact field equations are satisfied, to yield a spacetime with
equal amounts of ingoing and outgoing radiation.  Substantial parts of a
helically symmetric neutron-star code are now converging, but a fully
convergent code is not yet in hand. Results from recent neutron star
evolutions and their implications for gravitational-wave astronomy will
be discussed.