We present the results of a radial velocity survey designed to measure the
fraction of double degenerates among DA white dwarfs. The narrow core of th
e H alpha line was observed twice or more for 46 white dwarfs yielding radi
al velocities accurate to a few km s(-1). This makes our sun;ey the most se
nsitive to the detection of double degenerates undertaken to date. We found
no new double degenerates in our sample, though Ha emission from distant c
ompanions is seen in two systems. Two stars known to be double degenerates
prior to our observations are included in the analysis. We find a 95 per ce
nt probability that the fraction of double degenerates among DA white dwarf
s lies in the range [0.017, 0.19].