We investigate non-Gaussianity in general single field models without assuming slow-roll conditions or the exact scale invariance of the scalar power spectrum. The models considered include general single field inflation (e.g. Dirac-Born-Infeld and canonical inflation) as well as bimetric models. We compute the full non-Gaussian amplitude A, its size ƒNL, its shape, and the running with scale nNG. In doing so we show that observational constraints allow significant violations of slow-roll conditions and we derive explicit bounds on slow-roll parameters for fast-roll single field scenarios. A variety of new observational signatures is found for models respecting these bounds. We also explicitly construct concrete model implementations giving rise to this new phenomenology.