We show how toroidally compactified eleven-dimensional supergravity can be consistently truncated to yield a variety of maximally supersymmetric massive supergravities in space-time dimensions D ⩽ 8. The mass terms arise as a consequence of making a more general ansatz than that in usual Kaluza-Klein dimensional reduction, in which one or more axions are given an additional linear dependence on one of the compactification coordinates. The lower-dimensional theories are nevertheless consistent truncations of eleven-dimensional supergravity. Owing to the fact that the generalised reduction commutes neither with U-duality nor with ordinary dimensional reduction, many different massive theories can result. The simplest examples arise when just a single axion has the additional linear coordinate dependence. We find five inequivalent such theories in D = 7, and 71 inequivalent ones in D = 4. The massive theories admit no maximally symmetric vacuum solution, but they do admit (D - 2)-brane solutions, i.e. domain walls, which preserve half the supersymmetry. We present examples of these solutions, and their oxidations to D = 11. Some of the latter are new solutions of D = 11 supergravity.