  We introduce a special class of pairwise-independent self-joinings for a
stationary process: Those for which one coordinate is a continuous function of
the two others. We investigate which properties on the process the existence of
such a joining entails. In particular, we prove that if the process is
aperiodic, then it has positive entropy. Our other results suggest that such
pairwise independent, non-independent self-joinings exist only in very specific
situations: Essentially when the process is a subshift of finite type
topologically conjugate to a full-shift. This provides an argument in favor of
the conjecture that 2-fold mixing implies 3-fold-mixing.
