We present and investigate a model for layered superconductors with single-electron interlayer tunneling and a unit cell containing an arbitrary number of sheets. For an effective pairing of two-dimensional origin, Tc is found to be independent of the layer spacings. However, pairing of three-dimensional nature, allowing for spacing dependent coupling strength, fits remarkably well the observed climb in Tc for the Bi-O and Tl-O layered systems, as the number of CuO2 planes in the unit cell is increased from two to four and six. This agreement points to a weak coupling pairing mechanism of three-dimensional origin. © 1988 Springer-Verlag.