We studied, theoretically, the optical absorption spectra for a slightly asymmetric double quantum well (DQW), in the presence of electric and magnetic fields. Recent experimental results for a 10.18/3.82/9.61 nm GaAs/Al_0.33Ga_0.67As DQW show clearly the different behaviours of the luminescence peaks for the indirect exciton IX and left direct exciton DX as functions of the external electric field. We show that the presence of a peak near the DX peak attributed to an impurity-bound left DX in the experimental results could be a consequence of non-trivial mixing between excitonic states.