  This paper tries to establish whether there are variations of the central
wavelengths or the profile shapes of diffuse interstellar bands (DIBs) and
whether these variations are caused by different physical parameters of
translucent clouds.
  For this purpose we used spectra of two stars seen through two different
single clouds: HD34078 (AE Aur) \& HD73882 acquired using
  two different instruments: the MIKE spectrograph, fed with the 6.5 m Magellan
telescope at Las Campanas Observatory, and the UVES, fed with the 8 m Kueyen
telescope at the Paranal observatory. The wavelength displacements of the DIBs
at 6196, 6203, 6376, 6379 and 6614 \AA\ with respect to the well known
interstellar atomic and molecular lines (K{\sc i} and CH) have been measured.
The mentioned shift is seemingly absent in the DIBs at 4726, 4964, 4763, and
4780 \AA. In addition the considered profiles may show (in HD34078) extended
red wings. The observed phenomena are likely related to physical parameters of
intervening clouds (rotational temperatures of molecular species) and may help
in the identification of the DIB carriers.
