We present the results of radial velocity measurements of 770 thick disk red giants toward the South Galactic Pole , vertically distributed from 0.5 kpc to 5 kpc with respect to the Galactic plane . We find a small gradient in the vertical velocity dispersion ( \sigma _ { W } ) of 3.8 \pm 0.8 km s ^ { -1 } kpc ^ { -1 } . Even more noteworthy , our values of \sigma _ { W } are small compared to literature values : in the middle of the vertical height range we find \sigma _ { W, \mathrm { z = 2 kpc } } =30 km s ^ { -1 } . We found no possible explanation for this small value of \sigma _ { W } in terms of sample contamination by thin disk stars , nor by wrong assumptions regarding the metallicity distribution and the derived distances .