For a variety of diffeomorphism-invariant field theories describing hy
persurface motions (such as relativistic M-branes in spacetime dimensi
on M+2) we perform a Hamiltonian reduction 'at level 0', showing that
a simple algebraic function of the normal velocity is canonically conj
ugate to the shape Sigma of the hypersurface. The Hamiltonian dependen
ce on Sigma is solely via the domain of integration, raising hope for
a consistent, reparametrization-invariant quantization.