A comparative study of fundamental (N = 1) bright solitons is carried out numerically in models for pulse propagation in semiconductor-doped fibres. In particular, the effect of averaging over the cross section of the fibre on the characteristics of the solitons is analysed in commonly used models with exponential and fractional forms of nonlinear saturation. It is shown that the averaged as well as unaveraged models contain two-state soliton solutions in the sense that for a given set of fibre parameters there exist two soliton solutions with the same width but different amplitude and hence different peak powers and shapes. The stability of the solitons and the effect of fibre dissipation on them are also analysed.