  We extend the class of factorization theorems for non-global observables from
fixed angular constraints to cross sections defined in terms of sequential jet
clustering. The associated hard and soft functions depend not only on the
directions of the hard partons, but also on their energy fractions. We derive
the one-loop anomalous dimension of the hard functions that drives the
leading-logarithmic resummation. The anomalous dimension imposes energy
ordering, which simplifies the clustering sequence. We perform resummations for
gap-between-jet observables defined with different jet algorithms and explain
the effects of the clustering on the importance of secondary emissions and on
the effective gap size.
