A novel and fast time‐domain quantitation algorithm—quantitation based on semi‐parametric quantum estimation (QUEST)—invoking optimal prior knowledge is proposed and tested. This nonlinear least‐squares algorithm fits a time‐domain model function, made up from a basis set of quantum‐mechanically simulated whole‐metabolite signals, to low‐SNR in vivo data. A basis set of in vitro measured signals can be used too. The simulated basis set was created with the software package NMR‐SCOPE which can invoke various experimental protocols. Quantitation of ¹H short echo‐time signals is often hampered by a background signal originating mainly from macromolecules and lipids. Here, we propose and compare three novel semi‐parametric approaches to handle such signals in terms of bias‐variance trade‐off. The performances of our methods are evaluated through extensive Monte‐Carlo studies. Uncertainty caused by the background is accounted for in the Cramér–Rao lower bounds calculation. Valuable insight about quantitation precision is obtained from the correlation matrices. Quantitation with QUEST of ¹H in vitro data, ¹H in vivo short echo‐time and ³¹P human brain signals at 1.5 T, as well as ¹H spectroscopic imaging data of human brain at 1.5 T, is demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.