With the HOD molecule initially in its vibrational ground state, we theoretically analyze the laser-induced control of the OD/OH branching ratio D+OH <- HOD -> H+OD in the first absorption band. In the weak-field limit, any form of UV-pulse shaping control leads to a branching ratio larger than similar to 2. We obtain in the strong-field limit (peak intensities similar to 10 TW/cm(2)) a branching ratio significantly less than 2. The optimized pulses operate by a pump-dump-pump mechanism, where the dumping to the electronic ground state creates nonstationary vibrational states in HOD.