Highly effective water suppression schemes were designed on the basis of repetition of the sequence of a chemical-shift-selective RF pulse followed by a dephasing gradient pulse (CHESS) (A. Haase, J. Frahm, W. Haenicke, and D. Matthei, Phys. Med. Biol., 30, 341, 1985). These repeated CHESS sequences are constructed to avoid the occurrence of unwanted echoes. Implementation in the stimulated echo sequence is described in theory and experiment. The efficiency of the suppression is demonstrated in a phantom, as well as in vivo for cat brain and human brain. Routinely, suppression factors of more than 10,000 were obtained, even in the unfavorable case of a surface coil transmitter. This enables the acquisition of short echo time, localized proton spectra in vivo with optimal dynamic range and without phase or intensity roll over the spectrum. Relaxation and displacement effects are discussed. The potential of these techniques for high-resolution NMR is evaluated.