A comparative study of low-Re wall-distance-free (WDF) turbulence models in incompressible flows is presented. The study includes the WDF k-ϵ and the three-equation WDF k-ϵ-γ as well as two k-ϵ models which invoke the distance from the wall. The models are implemented in conjunction with a characteristics-based method and an implicit unfactored scheme. Comparison with direct-numerical-simulation data reveals that the WDF models provide much more accurate results for the dissipation rate, especially in the near wall region. A grid refinement study further reveals that the models which explicitly involve the distance from the wall cannot capture the correct turbulence dissipation rate behaviour in the near-wall region even on the finest grid, where grid-independent solution is achieved. However, the low-Re WDF models require slightly more iterations than the other k - ϵ models to converge. Results are presented for channel, flat plate and backward-facing step flows.