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EXSY, TOCSY and NOESY lie at the foundation of homonuclear NMR experiments in organic and pharmaceutical chemistry, as well as in structural biology. Limited magnetization transfer efficiency is an intrinsic downside of these methods, particularly when targeting rapidly exchanging species such as labile protons ubiquitous in polysaccharides, sidechains and backbones of proteins, and in bases and sugars of nucleic acids: the fast decoherence imparted on these protons through solvent exchanges, greatly reduces their involvement in homonuclear correlation experiments. We have recently discussed how these decoherences can be visualized as an Anti-Zeno Effect, that can be harnessed to enhance the efficiency of homonuclear transfers within Looped PROjected SpectroscopY (L-PROSY) leading to 200-300% enhancements in NOESY and TOCSY cross-peaks for amide groups in biomolecules. This study demonstrates that even larger sensitivity gains per unit time, equivalent to reductions by several hundred-folds in the duration of experiments, can be achieved by looping inversion or using saturation procedures. In the ensuing experiments a priori selected frequencies are encoded according to Hadamard recipes, and subsequently resolved along the indirect dimension via linear combinations. Magnetization-transfer (MT) processes reminiscent of those occurring in CEST provide significant enhancements in the resulting cross-peaks, in only a fraction of acquisition time of a normal 2D experiment. The effectiveness of the ensuing three-way polarization transfer interplay between water, labile and non-labile protons was corroborated experimentally for proteins, homo-oligosaccharides and nucleic acids. In all cases, cross-peaks barely detectable in conventional 2D NMR counterparts, were measured ca. 10-fold faster and with 200-600% signal enhancements by the Hadamard MT counterparts.