  Context. Copper is an element whose interesting evolution with metallicity is
not fully understood. Observations of copper abundances rely on a very limited
number of lines, the strongest are the Cu I lines of Mult. 1 at 324.7 nm and
327.3 nm which can be measured even at extremely low metallicities. Aims. We
investigate the quality of these lines as abundance indicators. Method. We
measure these lines in two turn-off (TO) stars in the Globular Cluster NGC 6752
and two TO stars in the Globular Cluster NGC 6397 and derive abundances with 3D
hydrodynamical model atmospheres computed with the CO5BOLD code. These
abundances are compared to the Cu abundances measured in giant stars of the
same clusters, using the lines of Mult. 2 at 510.5 nm and 578.2 nm. Results.
The abundances derived from the lines of Mult. 1 in TO stars differ from the
abundances of giants of the same clusters. This is true both using CO5BOLD
models and using traditional 1D model atmospheres. The LTE 3D corrections for
TO stars are large, while they are small for giant stars. Conclusions. The Cu I
resonance lines of Mult. 1 are not reliable abundance indicators. It is likely
that departures from LTE should be taken into account to properly describe
these lines, although it is not clear if these alone can account for the
observations. An investigation of these departures is indeed encouraged for
both dwarfs and giants. Our recommendation to those interested in the study of
the evolution of copper abundances is to rely on the measurements in giants,
based on the lines of Mult. 2. We caution, however, that NLTE studies may imply
a revision in all the Cu abundances, both in dwarfs and giants.
