A previously developed approach for the computation of optimal laser pulses in the weak-field limit is extended to systems undergoing dephasing and dissipation and thus requiring a density matrix treatment. The starting point is a multicolor gaussian pulse which can be shaped by modifying its individual amplitudes and phases. The method is grounded on the generation of random pulses to form a linearly-independent basis set from which the optimal pulse is determined by linear algebra manipulations. As an interesting example we show that the coherent component of the fluorescence (free induction decay, FID) from the B850 ring present in the light-harvesting 2 (LH2) complex of the purple bacterium Rhodopseudomonas acidophila can be significantly enhanced. The calculations have been performed using a Redfield equation built up from a model Frenkel Hamiltonian taken from the literature with a phenomenological dephasing time for electronic coherences. (C) 2003 Published by Elsevier B.V.