It is shown that new parameters X can be defined such that the heat capacity C{sub X} {equivalent to} T({partial derivative}S/{partial derivative}T)X is negative, even when the canonical ensemble (i.e. at fixed T = ({partial derivative}U/{partial derivative}S) and Y {ne} X) is stable. As examples we treat black body radiation and general gas systems with nonsingular {kappa}{sub T}. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p,V) = const. that makes C{sub X} < 0. Since it is possible to invent constraints for which canonically stable systems have negative heat capacity we speculate that it may also be possible to infer the statistical mechanics of canonically unstable systems - for which even the traditional heat capacities are negative - by imposing constraints that stabilize the associated, inoncanonical ensembles.