  The maximally supersymmetric type IIB pp-wave is compactified on spatial
circles, with and without an auxiliary rotational twist. All spatial circles of
constant radius are identified. Without the twist, an S$^1$ compactification
can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve
20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16
supercharges and higher compactifications preserve 16 supercharges. The
worldsheet theory of this background is discussed. The T-dual and
decompactified type IIA and M-theoretic solutions which preserve 24
supercharges are given. Some comments are made regarding the AdS parent and the
CFT description.
