It is commonplace that NMR echo maxima appear at times for which the dephasing and the rephasing periods of a pulse sequence are equally long. However, for stimulated echoes a significant time shift from this naively expected echo position can be observed if the dephasing times are smaller than the inverse line width of the NMR spectrum. This effect, which will be observable for any line shape, is evaluated quantitatively for Gaussian and for Pake-like patterns. Comparison of the calculations is made with experimental results from (6)Li- and from (2)H-NMR and excellent agreement is found. In the simultaneous presence of broad and narrow lines, the apparent time shift can give rise to characteristic distortions in spin-alignment spectra. This explains some features previously observed using (7)Li-NMR.