  We describe a directed search for continuous gravitational waves in data from
the sixth LIGO science run. The target was the nearby globular cluster NGC 6544
at a distance of 2.7 kpc. The search covered a broad band of frequencies along
with first and second frequency derivatives for a fixed sky position. The
search coherently integrated data from the two LIGO interferometers over a time
span of 9.2 days using the matched-filtering F-statistic. We found no
gravitational-wave signals and set 95% confidence upper limits as stringent as
6.0 X 10^{-25} on intrinsic strain and 8.5 X 10^{-6} on fiducial ellipticity.
These values beat the indirect limits from energy conservation for stars with
characteristic spindown ages older than 300 years and are within the range of
theoretical predictions for possible neutron-star ellipticities. An important
feature of this search was use of a barycentric resampling algorithm which
substantially reduced computational cost; this method will be used extensively
in searches of Advanced LIGO and Virgo detector data.
