We present broadband optical polarimetry of the classical novae V705 Cas, V4362 Sgr, V2313 Oph and BY Cir in outburst. The data indicate that, in all cases, there is an intrinsic component of polarization and in some cases the variability is very rapid, on a time-scale ~1day. In the case of V705 Cas, we suggest that the origin of the intrinsic component may lie in the clumpiness and/or inhomogeneities of the ejecta, while electron scattering is the most likely cause in V2313 Oph. The wavelength-dependence of polarization in the case of V4362 Sgr suggests scattering by small dust grains, while polarization in resonance lines is the most probable cause of the observed polarization in BY Cir.