An implantable cuff electrode and/or optrode adapted to encircle a substantially cylindrical tissue, and comprising: • a support sheet which, when deployed on a flat surface, comprises first and second longitudinal edges extending parallel to a transverse axis, wherein the support sheet is non-conductive and is rolled about a longitudinal axis, normal to the transverse axis, thus forming a cuff of substantially cylindrical or helical geometry defining a lumen extending over a length, along the longitudinal axis, of substantially constant inner diameter (Dc), measured along a radial axis, normal to the longitudinal axis, wherein said cuff comprises, ∘ an inner surface forming an interior of the cuff, and an outer surface forming an exterior of the cuff, separated from the inner surface by a thickness of the cuff, ∘ a central portion, extending over a length (Ic), of at least 50% of the length of the cuff, and having a mean central thickness (tc), measured normal to the longitudinal axis, and wherein the central portion is flanked on either side by, ∘ a first edge portion extending from a first free edge of the cuff to the central portion along the longitudinal axis, and a second edge portion extending from a second free edge of the cuff to the central portion along the longitudinal axis, wherein the first free edge portion has a mean edge thickness, and the second free edge portion has a mean edge thickness, • at least a first electrode contact made of a conductive material exposed at the inner surface of the cuff, and being remote from the outer surface forming the exterior of the cuff, and/or • at least a first optical contact (60, 601a-601c) for guiding a light beam from the inner surface towards the longitudinal axis, Characterized in that, the mean edge thicknesses (te1, te2) of the first and second edge portions are each lower than the mean central thickness (tc) (te1 < tc and te2 < tc), and in that, the inner surface of the cuff extends beyond the central outer surface in both directions along the longitudinal axis. • a support sheet which, when deployed on a flat surface, comprises first and second longitudinal edges extending parallel to a transverse axis, wherein the support sheet is non-conductive and is rolled about a longitudinal axis, normal to the transverse axis, thus forming a cuff of substantially cylindrical or helical geometry defining a lumen extending over a length, along the longitudinal axis, of substantially constant inner diameter (Dc), measured along a radial axis, normal to the longitudinal axis, wherein said cuff comprises, ∘ an inner surface forming an interior of the cuff, and an outer surface forming an exterior of the cuff, separated from the inner surface by a thickness of the cuff, ∘ a central portion, extending over a length (Ic), of at least 50% of the length of the cuff, and having a mean central thickness (tc), measured normal to the longitudinal axis, and wherein the central portion is flanked on either side by, ∘ a first edge portion extending from a first free edge of the cuff to the central portion along the longitudinal axis, and a second edge portion extending from a second free edge of the cuff to the central portion along the longitudinal axis, wherein the first free edge portion has a mean edge thickness, and the second free edge portion has a mean edge thickness, ∘ an inner surface forming an interior of the cuff, and an outer surface forming an exterior of the cuff, separated from the inner surface by a thickness of the cuff, ∘ a central portion, extending over a length (Ic), of at least 50% of the length of the cuff, and having a mean central thickness (tc), measured normal to the longitudinal axis, and wherein the central portion is flanked on either side by, ∘ a first edge portion extending from a first free edge of the cuff to the central portion along the longitudinal axis, and a second edge portion extending from a second free edge of the cuff to the central portion along the longitudinal axis, wherein the first free edge portion has a mean edge thickness, and the second free edge portion has a mean edge thickness, • at least a first electrode contact made of a conductive material exposed at the inner surface of the cuff, and being remote from the outer surface forming the exterior of the cuff, and/or • at least a first optical contact (60, 601a-601c) for guiding a light beam from the inner surface towards the longitudinal axis,