  Given a spherical spacelike three-geometry, there exists a very simple
algebraic condition which tells us whether, and in which, Schwarzschild
solution this geometry can be smoothly embedded. One can use this result to
show that any given Schwarzschild solution covers a significant subset of
spherical superspace and these subsets form a sequence of nested domains as the
Schwarzschild mass increases. This also demonstrates that spherical data offer
an immediate counter example to the thick sandwich `theorem'.
