Conformationally restricted amino acids are promising candidates to serve as basic pieces in redesigned protein motifs which constitute the basic modules in synthetic nanoconstructs. Here we study the ability of constrained cyclic amino acid 1-aminocyclohexane-1-carboxylic acid (Ac6c) to stabilize highly regular β-helical motifs excised from naturally occurring proteins. Calculations indicate that the conformational flexibility observed in both the ring and the main chain is significantly higher than that detected for other 1-aminocycloalkane-1-carboxylic acids (Acnc, where n refers to the size of the ring) with smaller cycles. Incorporation of Ac6c into the flexible loops of β-helical motifs indicates that the stability of such excised building blocks as well as the nanoassemblies derived from them is significantly enhanced. Thus, the intrinsic Ac6c tendency to adopt folded conformations combined with the low structural strain of the cyclohexane ring confers the ability to both self-adapt to the β-helix motif and to stabilize the overall structure by absorbing part of its conformational fluctuations. Comparison with other Acnc residues indicates that the ability to adapt to the targeted position improves considerably with the ring size, i.e., when the rigidity introduced by the strain of the ring decreases.