The conformational landscapes of p53 peptide variants and phage derived peptide (12/1) variants, all known to bind to MDM2, are studied using hamiltonian replica exchange molecular dynamics simulations. Complementing earlier observations, the current study suggests that the p53 peptides largely follow the 'conformational selection' paradigm in their recognition of and complexation by MDM2 while the 12/1 peptides likely undergo some element of conformational selection but are mostly driven by 'binding induced folding'. This hypothesis is further supported by pulling simulations that pull the peptides away from their bound states with MDM2. This data extends the earlier mechanisms proposed to rationalize the entropically driven binding of the p53 set and the enthalpically driven binding of the 12/1 set. Using our hypothesis, we suggest mutations to the 12/1 peptide that increase its helicity in simulations and may, in turn, shift the binding towards conformational selection. In summary, understanding the conformational landscapes of the MDM2-binding peptides may suggest new peptide designs with bespoke binding mechanisms.