We observed a small sample of five radio-quiet quasars with integral field spectroscopy to search for possible extended emission in the Lyα line. We subtracted the quasar point sources using a simple point spread function (PSF) self-calibration technique that takes advantage of the simultaneous availability of spatial and spectral information. In four of the five objects we find no significant traces of extended Lyα emission beyond the contribution of the quasar nuclei itself, while in UM 247 there is evidence for a weak and spatially quite compact excess in the Lyα line at several kpc outside the nucleus. For all objects in our sample we estimated detection limits for extended, smoothly distributed Lyα 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 Lyα nebulae such as those found recently around some quasars are very rare. Lyα fuzz around typical radio-quiet quasars is fainter and less extended and is therefore much harder to detect. The faintness of these structures is consistent with the idea that radio-quiet quasars typically reside in dark matter haloes of modest masses.Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).