  We classify and construct all the smooth Kaluza-Klein reductions to ten
dimensions of the M2- and M5-brane configurations which preserve some of the
supersymmetry. In this way we obtain a wealth of new supersymmetric IIA
backgrounds describing composite configurations of D-branes, NS-branes and
flux/nullbranes; bound states of D2-branes and strings, D4-branes and
NS5-branes, as well as some novel configurations in which the quotient involves
nowhere-vanishing transverse rotations to the brane twisted by a timelike or
lightlike translation. From these results there also follow novel M-theory
backgrounds locally isometric to the M-branes, some of which are time-dependent
and all of which are asymptotic to discrete quotients of eleven-dimensional
Minkowski spacetime. We emphasise the universality of the formalism by briefly
discussing analogous analyses in type IIA/IIB dual to the ones mentioned above.
Some comments on the dual gauge theory description of some of our
configurations are also included.
