  The Gray-Wyner network subject to a fidelity criterion is studied. Upper and
lower bounds for the trade-offs between the private sum-rate and the common
rate are obtained for arbitrary sources subject to mean-squared error
distortion. The bounds meet exactly, leading to the computation of the rate
region, when the source is jointly Gaussian. They meet partially when the
sources are modeled via an additive Gaussian "channel". The bounds are inspired
from the Shannon bounds on the rate-distortion problem.
