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