  The efficiency and cooling power of a two-terminal thermoelectric
refrigerator are analyzed near the limit of vanishing dissipation (ideal
system), where the optimal efficiency is the Carnot one, but the cooling power
then unfortunately vanishes. This limit, where transport occurs only via a
single sharp electronic energy, has been referred to as "strong coupling" or
"the best thermoelectric". It follows however, that "parasitic" effects that
make the system deviate from the ideal limit, and reduce the efficiency from
the Carnot limit, are crucial for the usefulness of the device. Among these
parasitics, there are: parallel phonon conduction, finite width of the
electrons' transport band and more than a single energy transport channel. In
terms of a small parameter characterizing the deviation from the ideal limit,
the efficiency and power grow linearly, and the dissipation {\em
quadratically}. The results are generalized to the case of broken time-reversal
symmetry, and the major nontrivial changes are discussed. Finally, the recent
universal relation between the thermopower and the asymmetry of the dissipation
between the two terminals is briefly discussed, including the small dissipation
limit.
