  Current estimates for white dwarfs with fields in excess of 1MG are about
10%; according to our first high-precision circular-polarimetric study of 12
bright white dwarfs with the VLT (Aznar Cuadrado et al. 2004) this number
increases up to about 25% in the kG regime. With our new sample of 10 white
dwarf observations (plus one sdO star) we wanted to improve the sample
statistics to determine the incident of kG magnetic fields in white dwarfs. In
one of our objects (LTT7987) we detected a statistically significant (97%
confidence level) longitudinal magnetic field varying between (-1+-0.5)kG and
(+1+-0.5$)kG. This would be the weakest magnetic field ever found in a white
dwarf, but at this level of accuracy, systematic errors cannot completely be
ruled out. Together with previous investigations, the fraction of kG magnetic
fields in white dwarfs amounts to about 11-15%, which is close to the current
estimations for highly magnetic white dwarfs (>1MG).
