A computational strategy for the deconvolution of complex spectra involving scalar multiplet patterns is presented. This approach fits spectra that can be composed of single resonances as well as scalar coupling multiplets for which resonance frequencies, intensities, and lineshape parameters can be optimized. For multiplets, the coupling constant also is optimized. Any external information about the optimizable parameters can be taken into account as external constraints. A lineshape described by absorptive and dispersive Lorentzian and Gaussian contributions and the baseline with up to 40 Fourier and polynomial terms can likewise be optimized. The effectiveness of the procedure is assessed on the basis of computer simulated deconvolutions of a composite of 1J(13C-2H) multiplets arising from a mixture of all possible 13C-2H isotopomers of deuterated L-[3-13C]lactate generated from cell preparations incubated with D-[1-13C]glucose in D2O, which was analyzed previously with a manual deconvolution procedure (R. Willem, M. Biesemans, F. Kayser, W. J. Malaisse, Magn, Reson. Med. 31, 259-267 (1994)). The use of constraints is shown to lead to an improvement in the results. The fitting strategies and the importance of the baseline as an origin of bias are discussed.