Buckling of compressed flat-end columns loaded by unattached flat platens is shown, theoretically and experimentally, to occur first at the critical load and associated mode shape of a built-in column, followed extremely closely by a second critical load and different mode shape characterized by column end tilt. The theoretical critical load for secondary or end tilt buckling for a column geometry tested is shown to be only 0.13% greater than the critical load for primary buckling, in which the ends are in full contact with the compression platens. The experimental value is consistent with this theoretical one. Interestingly, under displacement control, the first buckling instability is characterized by a smoothly increasing applied load, whereas the closely following second instability causes an abrupt and large load drop (and hence exhibits incremental negative stiffness). The end tilt buckling gives rise to large hysteresis that can be useful in structural damping but that is nonconservative and potentially catastrophic in the context of design of structural support columns.