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(abridged) We propose the new designation ``WNH'' for luminous Wolf-Rayet(WR) stars of the nitrogen sequence with H in their spectra. These are commonlycalled WNL stars (e.g., WN7h), but this new shorthand avoids confusion becausethere are late-type WN stars without H and early-type WN stars with H. Clearlydifferentiating WNH stars from H-free WN stars is critical when discussingprogenitors of Type Ib/c SNe and GRBs -- the massive WNH stars are not likelySN progenitors, and are distinct from core-He burning WR stars. We show thatthe masses of WNH stars are systematically higher than H-poor WR stars (both WNand WC), with little overlap, while H mass fractions of luminous WNH starsexceed those of LBVs. We favor the interpretation that the most luminous WNHstars are still core-H burning, pre-LBVs. While on the main sequence, a star'smass is reduced due to winds while its luminosity slowly rises, so the starincreases its Eddington factor and mass-loss rate, pushing it even closer tothe Eddington limit. With this feedback, observed masses and mass-loss rates ofWNH stars are a natural outcome near the end of core-H burning. Feedback fromthe strong WNH wind itself then enables the instability seen later as an LBV.Steadily climbing mass-loss rates also explain continuity in spectral traitsfrom O3 V to O3 If* to WNH.

On the role of the WNH phase in the evolution of very massive stars: Enabling the LBV instability with feedback