QCD sum rules for vector mesons (rho, omega, phi) in nuclear matter ar
e reexamined with an emphasis on the reliability of various sum rules.
Monitoring the continuum contribution and the convergence of the oper
ator product expansion plays a crucial role in determining the validit
y of a sum rule. The uncertainties arising from less than precise know
ledge of the condensate values and other input parameters are analyzed
via a Monte Carlo error analysis. Our analysis leaves no doubt that v
ector-meson masses decrease with increasing density. This resolves the
current debate over the behavior of the vector-meson masses and the s
um rules to be used in extracting vector meson properties in nuclear m
atter. We find a ratio of rho-meson masses of m(rho)/m(rho)=0.78+/-0.
08 at nuclear matter saturation density.