The transport theory of an axisymmetric toroidal low-β plasma in the collision-dominated regime is extended to collision frequencies higher and Larmor radii larger than admissible in the usual Pfirsch-Schlüter regime. Important modifications of the particle and heat fluxes are found. In particular, the toroidal enhancement of the ion heat flux turns out to be decreased with respect to the Pfirsch-Schlüter value outside this regime. For high collision frequencies, a toroidal enhancement of the pinch effect, quantitatively analogous to the Ware effect, appears. A necessary condition for the validity of the theory exposed is that the radial heat flux of the ions is larger than that of the electrons.