  Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding
walks in the upper half plane, we show that the conjectured scaling limit of
the half-plane SAW, the SLE(8/3) process, also has an appropriately defined
bridge decomposition. This continuum decomposition turns out to entirely be a
consequence of the restriction property of SLE(8/3), and as a result can be
generalized to the wider class of restriction measures. Specifically we show
that the restriction hulls with index less than one can be decomposed into a
Poisson Point Process of irreducible bridges in a way that is similar to Ito's
excursion decomposition of a Brownian motion according to its zeros.
