  The presence of long-ranged correlations in a fluid undergoing uniform shear
flow is investigated. An exact relation between the density autocorrelation
function and the density-mometum correlation function implies that the former
must decay more rapidly than $1/r$, in contrast to predictions of simple mode
coupling theory. Analytic and numerical evaluation of a non-perturbative
mode-coupling model confirms a crossover from $1/r$ behavior at ''small'' $r$
to a stronger asymptotic power-law decay. The characteristic length scale is
$\ell \approx \sqrt{\lambda_{0}/a}$ where $% \lambda_{0}$ is the sound damping
constant and $a$ is the shear rate.
