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The widths, dispersion measures, dispersion indices and fluences of FastRadio Bursts (FRB) impose coupled constraints that all models must satisfy.Observation of dispersion indices close to their low density limit of $-2$ setsa model-independent upper bound on the electron density and a lower bound onthe size of any dispersive plasma cloud. The non-monotonic dependence of burstwidths (after deconvolution of instrumental effects) on dispersion measureexcludes the intergalactic medium as the location of scattering that broadensthe FRB in time. Temporal broadening far greater than that of pulsars atsimilar high Galactic latitudes implies that scattering occurs close to thesources, where high densities and strong turbulence are plausible. FRBenergetics are consistent with supergiant pulses from young, fast, high-fieldpulsars at cosmological distances. The distribution of FRB dispersion measuresis inconsistent with expanding clouds (such as SNR). It excludes space-limiteddistributions (such as the local supercluster), but agrees with a homogeneouscosmological distribution with intergalactic dispersion. The FRB$\log{N}$--$\log{S}$ relation also indicates a cosmological distribution, asidefrom the anomalously bright Lorimer burst.

Inferences from the Distributions of Fast Radio Burst Pulse Widths, Dispersion Measures and Fluences