  We observed a small sample of 5 radio-quiet QSOs with integral field
spectroscopy to search for possible extended emission in the Ly$\alpha$ line.
We subtracted the QSO point sources using a simple PSF self-calibration
technique that takes advantage of the simultaneous availability of spatial and
spectral information. In 4 of the 5 objects we find no significant traces of
extended Ly$\alpha$ emission beyond the contribution of the QSO nuclei itself,
while in UM 247 there is evidence for a weak and spatially quite compact excess
in the Ly$\alpha$ line at several kpc outside the nucleus. For all objects in
our sample we estimated detection limits for extended, smoothly distributed
Ly$\alpha$ emission by adding fake nebulosities into the datacubes and trying
to recover them after PSF subtraction. Our observations are consistent with
other studies showing that giant Ly$\alpha$ nebulae such as those found
recently around some quasars are very rare. Ly$\alpha$ fuzz around typical
radio-quiet QSOs is fainter, less extended and is therefore much harder to
detect. The faintness of these structures is consistent with the idea that
radio-quiet QSOs typically reside in dark matter haloes of modest masses.
