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The interaction between human Growth Hormone (hGH) and hGH Receptor (hGHR) has basic relevance to cancer and growth disorders, and hGH is the scaffold for Pegvisomant, an anti-acromegaly therapeutic. For the latter reason, hGH has been extensively engineered by early workers to improve binding and other properties. We are particularly interested in E174 which belongs to the hGH zinc-binding triad; the substitution E174A is known to significantly increase binding, but to now no explanation has been offered. We generated this and several computationally-selected single-residue substitutions at the hGHR-binding site of hGH. We find that, while many successfully slow down dissociation of the hGH-hGHR complex once bound, they also slow down the association of hGH to hGHR. The E174A substitution induces a change in the Circular Dichroism spectrum that suggests the appearance of coiled-coiling. Here we show that E174A increases affinity of hGH against hGHR because the off-rate is slowed down more than the on-rate. For E174Y (and certain mutations at other sites) the slowdown in on-rate was greater than that of the off-rate, leading to decreased affinity. The results point to a link between structure, zinc binding, and hGHR-binding affinity in hGH.