  We present a reinterpretation of CMS searches for type-III seesaw lepton
triplets at the LHC, both for the normal and the inverse seesaw. We find that,
in contrast with previous expectations, these searches in the trilepton final
state have a good sensitivity to triplets with predominant coupling to the tau
lepton. We also show that the limits resulting from direct searches can be
neatly presented for arbitrary masses and general flavour mixings. Thus, it
turns out that the common (and often unrealistic) simplifying assumptions about
the flavour couplings of the triplets used by experimental collaborations to
present their results are unnecessary and should be dropped.
