  We report on new precision mass measurements of neutron-rich $^{137}$Sb and
$^{136-142}$I isotopes from the JYFLTRAP double Penning trap mass spectrometer.
We confirm the value from the previous Penning-trap measurement of $^{137}$Sb
at the Canadian Penning Trap and therefore rule out the conflicting result from
the Experimental Storage Ring. The ground state and isomer in $^{136}$I were
resolved and measured directly for the first time. The isomer excitation
energy, $E_x = 215.1(43)$ keV, agrees with the literature but is three times
more precise. The measurements have improved the precision of the mass values
and confirmed previous results in the majority of cases. However, for
$^{138,140}$I the results differ by 17(6) keV and 23(12) keV, respectively.
This could be explained by an unresolved contamination or different ratio of
unresolved isomeric states in the case of $^{140}$I.
