It is expected that hadron collider measurements of the Higgs boson mass using the decay h -> W^+W^-, followed by the leptonic decay of each W-boson, will be performed by fitting the shape of a distribution which is sensitive to the Higgs mass. We demonstrate that the variable most commonly used to measure the Higgs mass in this channel is not optimal as it contains an unnecessary and even counter-productive approximation. We remove that approximation, without introducing any cost in complexity, and demonstrate that the new variable is a clear improvement over the old: its performance is never worse, and in some cases (particularly the high Higgs mass region) it might reduce the fit uncertainty on the Higgs mass in that channel by a factor approaching two.