The need for understanding the winds of Wolf-Rayet (WR) stars cannot be understated: the light of these stars, their mass-loss rates, ionization capabilities and ultimately their further evolution is all greatly affected by the behaviour of their wind. Despite WR-star winds being notoriously difficult to model, advancements on this matter have been made. One approach is using non-LTE, co-moving frame computations with the Potsdam Wolf-Rayet (PoWR) code where now hydrodynamic consistency throughout the wind domain is enforced. While already applied multiple times for the regime of hot, hydrogen-free WR stars, we now present their first wide-range application in the regime of nitrogen-rich late-type WN stars that still contain hydrogen in their spectra (WNLh type). A newly generated temperature sequence of these WNLh-star models reveals a sudden change in the wind regimes: Below 30 kK, the mass-loss rates increase significantly, while the terminal wind velocity drops strongly, accompanied with large changes in the emergent model spectra. This discontinuous behaviour greatly resembles the well-known bi-stability jump in B-supergiants. Examining the models, we discover that our obtained regime change does not correspond to the switch from Fe IV to Fe III as expected, but is linked to the higher ionization switch of Fe V to Fe IV, therefore also coinciding with higher stellar temperatures. Hence, this bi-stable behaviour occurs both due to a different cause and in a different temperature regime as the "classical" case for B-supergiants, making it a different phenomenon altogether; a new bi-stability jump for Wolf-Rayet stars.