Fitting of model functions to low-SNR in vivo data with strongly overlapping peaks needs invocation of ever more prior knowledge about the model parameters. The fit can be performed in the frequency [1] or time [2] domain using measured spectra of selected metabolite solutions as numerical model functions. Alternatively, one can compute theoretical metabolite signals/spectra quantum-mechanically for the measurement protocol used by a scanner and fit in the frequency domain [3]. The proposed algorithm QUEST (QUantitation based on QUantum ESTimation) fits a combination of (quantum-mechanically simulated) signals of metabolites directly to the in vivo data at hand, in the time-domain domain. QUEST is based on • A non-linear least squares algorithm aiming at finding the model parameters that minimize the distance between the raw signal and the model function. This algorithm allows to automatically compensate for distortions due to the magnetic field heterogeneities with the ideal signals of the metabolite basis set. This has been done by using small extra damping factors and frequency shifts in the fit procedure. • A metabolite basis set. Signals of the metabolites were computed by quantum mechanics with NMR-SCOPE [4] using the spin Hamiltonian parameters given in [5]. NMR-SCOPE, based on the product-operator formalism, can handle various NMR pulse sequences. As for preprocessing, QUALITY deconvolution is applied first (if reference signal available), then water suppression using HLSVD [6] and macromolecule removal by weighting/truncation [7] or correction [8] of initial samples. The quantitation errors are estimated by computing the Cramer-Rao lower bounds. Note, that our CRBs are too small because we have not included the water/macromolecules in the model function. Results QUEST performances are assessed through Monte-Carlo studies, see Fig.1. Then, in vivo 1 H short echo-time signals of human brain at 1.5T obtained with STEAM were quantified with QUEST, see Fig.2. Signals of aspartate (Asp), choline (Cho), GABA, glucose, glutamate (Glu), glutamine (Gln), lactate (Lac), myo-inositol (Ins), Nacetylaspartate (NAA), phosphocreatine (PCr), creatine (Cr), taurine (Tau), plus signals modelling the lipids at 0.9 and 1.3 ppm were included in the QUEST fits. Quantitation of a 31 P signal is shown in Fig.3.