  We study the domain number and size distributions in the one-dimensional
Ising and $q$-state Potts models subject to zero-temperature Glauber dynamics.
The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted
domain, $Q_1(t)\sim t^{-\delta}$, are characterized by two independent
nonrtrivial exponents. For the Ising case, we find $\psi=0.126$ and
$\delta=1.27$ using numerical simulations. We develop an independent interval
approximation (IIA) that predicts the qualitative behavior of the domain
distribution and provides good estimates for the exponents. Exact results for
the domain distribution are also obtained in several solvable cases.
