  For thermoelectric transport in the presence of a magnetic field that breaks
time-reversal symmetry, a strong bound on the Onsager coefficients is derived
within a general set-up using three terminals. Asymmetric Onsager coefficients
lead to a maximum efficiency substantially smaller than the Carnot efficiency
reaching only \eta_C/4 in the limit of strong asymmetry. Related bounds are
derived for efficiency at maximum power, which can become larger than the
Curzon-Ahlborn value \eta_C/2, and for a cooling device. Our approach reveals
that in the presence of reversible currents the standard analysis based on the
positivity of entropy production is incomplete without considering the role of
current conservation explicitly.
