In ideal situations the gravity current fluid has a fixed density contrast to the ambient, ρc− ρa, and is enclosed in a well-defined, smooth, and impermeable envelope of volume V . In practical flows the density contrast and volume of the current may be reduced due to various effects. Overall, the global buoyancy |ρc/ρa− 1|gV decays with time. Here we consider some typical circumstances in which this decay of buoyancy is so severe that the inviscid current “runs out” of (most of) the driving effect and actually stops (or vanishes) after a finite distance of propagation. The viscous friction plays a minor role in the pertinent momentum balances.