  Einstein's field equations with cosmological constant are analysed for a
static, spherically symmetric perfect fluid having constant density. Five new
global solutions are described.
  One of these solutions has the Nariai solution joined on as an exterior
field. Another solution describes a decreasing pressure model with exterior
Schwarzschild-de Sitter spacetime having decreasing group orbits at the
boundary. Two further types generalise the Einstein static universe.
  The other new solution is unphysical, it is an increasing pressure model with
a geometric singularity.
