In experiments performed on protonated proteins at high fields, 80% of the NMR spectrometer time is spent waiting for the (1)H atoms to recover their polarization after recording the free induction decay. Selective excitation of a fraction of the protons in a large molecule has previously been shown to lead to faster longitudinal relaxation for the selected protons [K. Pervushin, B. Vögeli, A. Eletsky, Longitudinal (1)H relaxation optimization in TROSY NMR spectroscopy, J. Am. Chem. Soc. 124 (2002) 12898-12902; P. Schanda, B. Brutscher, Very fast two-dimensional NMR spectroscopy for real-time investigation of dynamic events in proteins on the time scale of seconds, J. Am. Chem. Soc. 127 (2005) 8014-8015; H.S. Attreya, T. Szyperski, G-matrix Fourier transform NMR spectroscopy for complete protein resonance assignment, Proc. Natl. Acad. Sci. USA 101 (2004) 9642-9647]. The pool of non-selected protons acts as a "thermal bath" and spin-diffusion processes ("flip-flop" transitions) channel the excess energy from the excited pool to the non-selected protons in regions of the molecule where other relaxation processes can dissipate the excess energy. We present here a sensitivity enhanced HSQC sequence (COST-HSQC), based on one selective E-BURP pulse, which can be used on protonated (15)N enriched proteins (with or without (13)C isotopic enrichment). This experiment is compared to a gradient sensitivity enhanced HSQC with a water flip-back pulse (the water flip-back pulse quenches the spin diffusion between (1)H(N) and (1)H(alpha) spins). This experiment is shown to have significant advantages in some circumstances. Some observed limitations, namely sample overheating with short recovery delays and complex longitudinal relaxation behaviour are discussed and analysed.