  Context. The identification of the carriers of diffuse interstellar bands
(DIBs) remains one of the long-standing mysteries in astronomy. The detection
of a polarisation signal in a DIB profile can be used to distinguish between a
dust or gas-phase carrier. The polarisation profile can give additional
information on the grain or molecular properties of the absorber. In order to
detect and measure the linear and circular polarisation of the DIBs we observed
reddened lines of sight showing continuum polarisation. For this study we
selected two stars HD 197770 and HD 194279. We used high-resolution (R~64.000)
spectropolarimetry in the wavelength range from 3700 to 10480 Angstrom with the
ESPaDOnS echelle spectrograph mounted at the CFHT.
  Results. High S/N and high resolution Stokes V (circular), Q and U (linear)
spectra were obtained. We constrained upper limits by a factor of 10 for
previously observed DIBs. Furthermore, we analysed ~30 additional DIBs for
which no spectropolarimetry data has been obtained before. This included the
9577 A DIB and the 8621 A DIB.
  Conclusions. The lack of polarisation in 45 DIB profiles suggests that none
of the absorption lines is induced by a grain-type carrier. The strict upper
limits, less than ~0.01%, derived for the observed lines-of-sight imply that if
DIBs are due to gas-phase molecules these carriers have polarisation
efficiencies which are at least 6 times, and up to 300 times, smaller than
those predicted for grain-related carriers.
