  We study a minimal stochastic model of step bunching during growth on a
one-dimensional vicinal surface. The formation of bunches is controlled by the
preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel
effect) and the ratio $d$ of the attachment rate to the terrace diffusion
coefficient. For generic parameters ($d > 0$) the model exhibits a very slow
crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$.
In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening
($\beta$ = 1) is observed instead. The different coarsening behaviors are
related to the fact that bunches attain a finite speed in the limit of large
size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$.
For $d=0$ an analytic description of the speed and profile of stationary
bunches is developed.
