  We discuss the vertical dimensional reduction of M-branes to domain walls in
D=7 and D=4, by dimensional reduction on Ricci-flat 4-manifolds and
7-manifolds. In order to interpret the vertically-reduced 5-brane as a domain
wall solution of a dimensionally-reduced theory in D=7, it is necessary to
generalise the usual Kaluza-Klein ansatz, so that the 3-form potential in D=11
has an additional term that can generate the necessary cosmological term in
D=7. We show how this can be done for general 4-manifolds, extending previous
results for toroidal compactifications. By contrast, no generalisation of the
Kaluza-Klein ansatz is necessary for the compactification of M-theory to a D=4
theory that admits the domain wall solution coming from the membrane in D=11.
