  It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points
if $\kappa>4$ and a.s. cutpoints if $4<\kappa<8$. If $\kappa>4$, an appropriate
version of $\SLE(\kappa)$ has a renewal property: it starts afresh after
visiting its frontier. Thus one can give an excursion decomposition for this
particular $\SLE(\kappa)$ ``away from its frontier''. For $4<\kappa<8$, there
is a two-sided analogue of this situation: a particular version of
$\SLE(\kappa)$ has a renewal property w.r.t its cutpoints; one studies
excursion decompositions of this $\SLE$ ``away from its cutpoints''. For
$\kappa=6$, this overlaps Vir\'ag's results on ``Brownian beads''. As a
by-product of this construction, one proves Watts' formula, which describes the
probability of a double crossing in a rectangle for critical plane percolation.
