We show experimental evidence of a new structure involving an
undercompressive and reverse undercompressive shock for draining films driven
by a surface tension gradient against gravity. The reverse undercompressive
shock is unstable to transverse perturbations while the leading
undercompressive shock is stable. Depending on the pinch-off film thickness, as
controlled by the meniscus, either a trailing rarefaction wave or a compressive
shock separates from the reverse undercompressive shock