It is shown that, given a few generic assumptions, any theory of high-temperature superconductivity that attributes a substantial fraction of the condensation energy to the saving of c-axis kinetic energy must predict an inequality relating the c-axis penetration depth lambda(perpendicular to)(0) to the zero-temperature superconducting-normal energy difference and the fluctuations of the c-axis kinetic energy around its mean value. Application of this formula to Tl2Ba2CuO6 implies that if lambda(perpendicular to)(0) is greater than 10 micrometers, as suggested by a recent experiment, these fluctuations must have an unusual form.