  We examine static perfect fluid spheres in the presence of a cosmological
constant. New exact matter solutions are discussed which require the Nariai
metric in the vacuum region. We generalize the Einstein static universe such
that neither its energy density nor its pressure is constant throughout the
spacetime. Using analytical techniques we derive conditions depending on the
equation of state to locate the vanishing pressure surface. This surface can in
general be located in regions with decreasing area group orbits. We use
numerical methods to integrate the field equations for realistic equations of
state and find consistent results.
