A monetary system called periodic re-coinage was used during almost 200 years in large part of medieval Europe. Old coins were frequently declared invalid and had to be exchanged for new ones for an exchange fee. This system – which is equivalent to a Gesell tax – required a limited coin volume in circulation and an exchange monopoly in a geographical area. We show that such a Gesell tax works and do generate incomes for the minting authority if the tax level is sufficiently low and if the punishment for using invalid coins is sufficiently high.