The kurtosis of a signal is a quantitative measure of how `peaky' it is. In this paper we consider two scenarios of communication over fading channels with kurtosis constraints: in the first, we analyze a non-coherent Rayleigh fading channel where the input signal is required to satisfy a kurtosis constraint in addition to a power constraint. In the second, we find the `worst' fading process that satisfies a kurtosis constraint and has a given second moment, while the fading coefficients are assumed to be known at the receiver. In both cases the transmitter is assumed ignorant of the instantaneous fading realization. The technique that enables our analysis is based on bounding mutual information between random variables which satisfy kurtosis and second moment constraints; the bound is tight in the low second moment regime and can be extended to multi-antenna communications.