  Current atmospheric models cannot reproduce some of the characteristics of
the transition between the L dwarfs with cloudy atmospheres and the T dwarfs
with dust-depleted photospheres. It has been proposed that a majority of the
L/T transition brown dwarfs could actually be a combinaison of a cloudy L dwarf
and a clear T dwarf. Indeed binarity seems to occur more frequently among L/T
transition brown dwarfs.
  We aim to refine the statistical significance of the seemingly higher
frequency of binaries. Co-eval binaries would also be interesting test-beds for
evolutionary models. We obtained high-resolution imaging for six mid-L to
late-T dwarfs, with photometric distances between 8 and 33pc, using the
adaptive optics systems NACO at the VLT, and the Lick system, both with the
laser guide star.
  We resolve none of our targets. Combining our data with published results, we
obtain a frequency of resolved L/T transition brown dwarfs of (31+21-15)%,
compared to (21+10-7)% and (14+14-7)% for mid-L and T dwarfs (90% of confidence
level). These fractions do not significantly support, nor contradict, the
hypothesis of a larger binary fraction in the L/T transition. None of our
targets has companions with effective temperatures as low as 360-1000K at
separations larger than 0.5".
