An implantable cuff electrode and/or optrode (40) adapted to encircle a substantially cylindrical tissue (70), is provided that includes a support sheet (43) rolled about a longitudinal axis, forming a cuff of inner diameter, Dc, and extending over a length, L a central portion, extending over a length, lc, of at least 50% of the length, L, and having a mean central thickness, tc, and wherein the central portion is flanked on either side by, a first edge portion (43e) of mean edge thickness, te1, and a second edge portion (43e) of mean edge thickness, te2, at least a first electrode contact or a first optrode exposed at an inner surface of the cuff, and remote from an outer surface forming the exterior of the cuff, Characterized in that, the mean edge thicknesses, te1, te2, of the first and second edge portions are each lower than tc.