Cyclopeptides (CPs) have been recognized as excellent templates for the rational design of biologically active compounds. However, in the absence of constraining elements, even the small cyclotetrapeptides (CTPs) and cyclopentapeptides (CPPs) may show conformational heterogeneity, with the occurrence of mixtures of cis/trans‐peptide bonds. In this paper, we discuss the synthesis of CTP and CPP model compounds containing 5‐aminomethyloxazolidine‐2,4‐dione (Amo)‐dipeptide scaffolds, which combine a β/α‐hybrid dipeptide structure & a Freidinger lactam‐like heterocycle. Depending on the stereochemistry, the dipeptide scaffolds were shown to efficiently promote well‐defined turn structures within the CP sequences, by taking advantage of the particular local constraints, and by establishing extra intramolecular hydrogen‐bonding interactions.