A major architectural class in engineered binding proteins ("antibody mimics") involves the presentation of recognition loops off a single-domain scaffold. This class of binding proteins, both natural and synthetic, has a strong tendency to bind a preformed cleft using a convex binding interface (paratope). To explore their capacity to produce high-affinity interfaces with diverse shape and topography, we examined the interface energetics and explored the affinity limit achievable with a flat paratope. We chose a minimalist paratope limited to two loops found in a natural camelid heavy-chain antibody (VHH) that binds to ribonuclease A. Ala scanning of the VHH revealed only three "hot spot" side chains and additional four residues important for supporting backbone-mediated interactions. The small number of critical residues suggested that this is not an optimized paratope. Using selection from synthetic combinatorial libraries, we enhanced its affinity by >100-fold, resulting in variants with Kd as low as 180 pM with no detectable loss of binding specificity. High-resolution crystal structures revealed that the mutations induced only subtle structural changes but extended the network of interactions. This resulted in an expanded hot spot region including four additional residues located at the periphery of the paratope with a concomitant loss of the so-called "O-ring" arrangement of energetically inert residues. These results suggest that this class of simple, single-domain scaffolds is capable of generating high-performance binding interfaces with diverse shape. More generally, they suggest that highly functional interfaces can be designed without closely mimicking natural interfaces.