We show that quantum optimal control theory (OCT) and time-dependent density-functional theory (TDDFT) can be combined to provide realistic femtosecond laser pulses for an enhanced ionization yield in few-electron systems. Using a one-dimensional model H₂ molecule as a test case, the optimized laser pulse from the numerically exact scheme is compared to pulses obtained from OCT+TDDFT within the TD exact-exchange (TDEXX) and the TD local-density approximation (TDLDA). We find that the TDDFT pulses produce an ionization yield of up to 50 per cent when applied to the exact system. In comparison, pulses with a single frequency but the same fluence typically reach to yields around 5 -15 per cent, unless the frequency is carefully tuned into a Fano-type resonance that leads to approximately 30 per cent yield. On the other hand, optimization within the exact system alone leads to yields higher than 80 per cent, demonstrating that correlation effects beyond the TDEXX and TDLDA can give rise to even more efficient ionization mechanisms.