The initial step of protein NMR resonance assignments typically identifies the sequence positions of H-1-N-15 HSQC cross-peaks. This is usually achieved by tediously comparing strips of multiple triple-resonance experiments. More conveniently, this could be obtained directly with hNcaNH and hNcocaNH-type experiments. However, in large proteins and at very high fields, rapid transverse relaxation severely limits the sensitivity of these experiments, and the limited spectral resolution obtainable in conventionally recorded experiments leaves many assignments ambiguous. We have developed alternative hNcaNH experiments that overcome most of these limitations. The TROSY technique was implemented for semiconstant time evolutions in both indirect dimensions, which results in remarkable sensitivity and resolution enhancements. Non-uniform sampling in both indirect dimensions combined with Maximum Entropy (MaxEnt) reconstruction enables such dramatic resolution enhancement while maintaining short measuring times. Experiments are presented that provide either bidirectional or unidirectional connectivities. The experiments do not involve carbonyl coherences and thus do not suffer from fast chemical shift anisotropy-mediated relaxation otherwise encountered at very high fields. The method was applied to a 300 mu M sample of a 37 kDa fragment of the E. coli enterobactin synthetase module EntF, for which high-resolution spectra with an excellent signal-to-noise ratio were obtained within 4 days each.