Rotating-frame NMR experiments which either emphasize or suppress cross relaxation, and which simultaneously suppress TOCSY, COSY, and zero-quantum peaks in NMR spectra, are presented and analyzed. The new experiments rely on mixing sequences which follow naturally from thetransverse-ROESY (Tr-ROESY) sequence of Hwang and Shaka, and which are applicable to larger molecules in solution (spin diffusion limit). In the first variant a modified Tr-ROESY sequence, called multiple-pulse ROESY (MP-ROESY), is used to enhance cross-relaxation peak intensity compared to Tr-ROESY; in the second, called phase-modulated CLEAN chemical exchange (CLEANEX-PM), cross-relaxation peaks are greatly attenuated. The two methods are thus complementary: MP-ROESY is used to observe Overhauser peaks, and CLEANEX-PM is used to eliminate them, permitting clear observation of chemical exchange peaks alone. The new techniques are examined by theory and experiment. Practical guidelines that will result in high-quality spectra are given, including the judicious use of continuous weak static magnetic field gradients.