Engineered peptides that bind with high affinity (low equilibrium dissociation constant (Kd)) to the cell surface receptors of fibronectin (α5β1) or vitronectin (αvβ3 and αvβ5 integrins) are disclosed. These peptides are based on a molecular scaffold into which a subsequence containing the RGD integrin-binding motif has been inserted. The subsequence (RGD mimic) comprises about 9-13 amino acids, and the RGD contained within the subsequence can be flanked by a variety of amino acids, the sequence of which was determined by sequential rounds of selection (in vitro evolution). The molecular scaffold is preferably based on a knottin, e.g., EETI (Trypsin inhibitor 2 (Trypsin inhibitor II) (EETI-II) [Ecballium elaterium (Jumping cucumber)], AgRP (Agouti-related protein), and Agatoxin IVB, which peptides have a rigidly defined three-dimensional conformation. It is demonstrated that EETI tolerates mutations in other loops and that the present peptides may be used as imaging agents.