  We report a new measurement of the CKM parameter V_ub made with a sample of
9.7 million B B-bar events collected with the CLEO II detector. Using Heavy
Quark theory, we combine the observed yield of leptons from semileptonic B
decay in the end-point momentum interval 2.2-2.6 GeV/c with recent CLEO II data
on B --> X_s gamma to find |V_ub| = (4.08 +/- 0.34 +/- 0.44 +/- 0.16 +/- 0.24)
x 10^-3, where the first two uncertainties are experimental and the last two
are from theory.
