Following a previous investigation in which the growth rates of tearing modes at weak instability were determined for a frequently used plasma model with convected resistivity, two further models are considered that appear to be more appropriate for realistic situations. In both of them viscosity is included. One has a self-consistently determined equilibrium resistivity that is kept constant during time evolution. In the other Spitzer resistivity is assumed, which, through its temperature dependence, evolves according to the energy law including thermal conductivity. All calculations are carried out for specific equilibria in a sheet pinch. A salient feature of the two models is the emergence of a stability threshold, which was not present in the previous model. Surprisingly, the results obtained for the two new models are almost the same, thus favouring the much simpler model with constant resistivity.