  The discrepancy between abundances computed using optical recombination lines
(ORLs) and collisionally excited lines (CELs) is a major unresolved problem in
nebular astrophysics. We show here that the largest abundance discrepancies are
reached in planetary nebulae with close binary central stars. This is
illustrated by deep spectroscopy of three nebulae with a post common-envelope
(CE) binary star. Abell 46 and Ou5 have O++/H+ abundance discrepancy factors
larger than 50, and as high as 300 in the inner regions of Abell 46. Abell 63
has a smaller discrepancy factor around 10, but still above the typical values
in ionized nebulae. Our spectroscopic analysis supports previous conclusions
that, in addition to "standard" hot (Te~10000 K) gas, a colder (Te~1000 K)
ionized component that is highly enriched in heavy elements also exists. These
nebulae have low ionized masses, between 0.001 and 0.1 solar masses depending
on the adopted electron densities and temperatures. Since the much more massive
red-giant envelope is expected to be entirely ejected in the CE phase, the
currently observed nebulae would be produced much later, in post-CE mass loss
episodes when the envelope has already dispersed. These observations add
constraints to the abundance discrepancy problem. Possible explanations are
revised. Some are naturally linked to binarity, such as for instance
high-metallicity nova ejecta, but it is difficult at this stage to depict an
evolutionary scenario consistent with all the observed properties. The
hypothesis that these nebulae are the result of tidal destruction, accretion
and ejection of Jupiter-like planets is also introduced.
