  We relate a Dp or NS-brane with D0-brane charge smeared over its worldvolume
to the system with no D0-charge. This allows us to generalise Reall's partial
proof of the Gubser-Mitra conjecture. We show explicitly for specific examples
that the dynamical instability coincides with thermodynamic instability in the
ensemble where the D0-brane charge can vary. We also comment on consistency
checks of the conjecture for more complicated systems, using the example of the
D4 with F1 and D0 charges smeared on its worldvolume.
