  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.
