The maximal acceleration corrections to the Lamb shift of one– electron atoms are calculated starting from the Dirac equation and splitting the spinor into large and small components. The results depend on Z8 and a cut-off Λ. Sizeable values are obtained even at Z = 1 for Λ ∼ a0/2, where a0 is the Bohr radius. These values are compatible with theoretical and experimental results. PACS: 04.90.+e, 12.20.Ds.