Rogoff has proposed to phase out paper currency to make economies cashless step by step. Such attempts that would start out with the calling-in of large-denomination banknotes could mitigate several social and economic problems like those posed by the effective lower bound on monetary policy rates. This paper provides theoretical evidence that the welfare gains from international coordination of calling-in moves could be substantial. We solve a stochastic stopping time game where two central banks choose exercise strategies for their `options' to call in large banknotes, and where decisions must be made under uncertainty about the future path of the natural rate of interest. The analysis shows, firstly, that a `wait-and-see'-value of the option to call in large notes will induce central banks to delay any calling-in moves, and secondly, that policy coordination will preserve this option value and will avoid welfare losses that result from suboptimal timing decisions.