  Our object of study is the general class of stick-breaking processes with
exchangeable length variables. These generalize well-known Bayesian
non-parametric priors in an unexplored direction. We give conditions to assure
the respective species sampling process is proper and the corresponding prior
has full support. For a rich sub-class we explain how, by tuning a single
$[0,1]$-valued parameter, the stochastic ordering of the weights can be
modulated, and Dirichlet and Geometric priors can be recovered. A general
formula for the distribution of the latent allocation variables is derived and
an MCMC algorithm is proposed for density estimation purposes.
