We discuss the difficulties of recovering the star formation history (SFH) of galaxies from their integrated light spectra. In a simplified mono-metallic unobscured linear case the conditioning number of the kernel (a time sequence of SSPs) indicates the feasibility of the inversion. We highlight two important pitfalls: (i) The quality of the SFH reconstructions artificially improves when increasing the noise in the SSP models, thus making it difficult to assess the reliability of the results in real life, (ii) Averaging the results of a large number of noisy SFH reconstructions does not constrain the underlying ``real'' SFH. We regularize the problem by imposing the smoothness and the positivity of the solutions. We perform a systematic study of the separation of superimposed double bursts, with free metallicity and extinction, in several pseudo-observational regimes. When the time elapsed between the two bursts is larger than .8 dex, their properties can be constrained with a precision of .04 dex in age and .02 dex in metallicity (not taking model errors into account) from high quality data R= 10000 and SNR= 100 per Å over the whole optical range.