  We find constraints on the generation of super-causal-horizon energy
perturbations from a smooth initial state, under a simple physical scheme. We
quantify these constraints by placing the upper limit $\lambda_c = 3.0 d_H$ on
the wavelength at which the power spectrum turns over to $k^4$ behavior. This
means that sub-horizon processes can generate significant power on scales
further outside the horizon than one might naively expect. The existence of
this limit may have important implications for the interpretation of the small
scale power spectrum of the Cosmic Microwave Background.
