  Small-x evolution in QCD is conveniently described by Mueller's dipole model
which, however, does not include saturation effects in a way consistent with
boost invariance. In this paper we first show that the recently studied zero
and one dimensional toy models exhibiting saturation and explicit boost
invariance can be interpreted in terms positive definite k-> k+1 dipole
vertices. Such k-> k+1 vertices can in the full model be generated by combining
the usual dipole splitting with k-1 simultaneous dipole swings. We show that,
for a system consisting of N dipoles, one needs to combine the dipole splitting
with at most N-1 simultaneous swings in order to generate all colour
correlations induced by the multiple dipole interactions.
