Combining computational and experimental tools, we present a new strategy for designing high affinity variants of a binding protein. The affinity is increased by mutating residues not at the interface, but at positions lining internal cavities of one of the interacting molecules. Filling the cavities lowers flexibility of the binding protein, possibly reducing entropic penalty of binding. The approach was tested using the interferon-γ receptor 1 (IFNγR1) complex with IFNγ as a model. Mutations were selected from 52 amino acid positions lining the IFNγR1 internal cavities by using a protocol based on FoldX prediction of free energy changes. The final four mutations filling the IFNγR1 cavities and potentially improving the affinity to IFNγ were expressed, purified, and refolded, and their affinity towards IFNγ was measured by SPR. While individual cavity mutations yielded receptor constructs exhibiting only slight increase of affinity compared to WT, combinations of these mutations with previously characterized variant N96W led to a significant sevenfold increase. The affinity increase in the high affinity receptor variant N96W+V35L is linked to the restriction of its molecular fluctuations in the unbound state. The results demonstrate that mutating cavity residues is a viable strategy for designing protein variants with increased affinity.