  We study a model of ``organized'' criticality, where a single avalanche
propagates through an \textit{a priori} static (i.e., organized) sandpile
configuration. The latter is chosen according to an i.i.d. distribution from a
Borel probability measure $\rho$ on $[0,1]$. The avalanche dynamics is driven
by a standard toppling rule, however, we simplify the geometry by placing the
problem on a directed, rooted tree. As our main result, we characterize which
$\rho$ are critical in the sense that they do not admit an infinite avalanche
but exhibit a power-law decay of avalanche sizes. Our analysis reveals close
connections to directed site-percolation, both in the characterization of
criticality and in the values of the critical exponents.
