Re-coinage implies that old coins are declared invalid and exchanged for new ones at fixed exchange rates and dates. Empirical evidence shows that re-coinage could occur as often as twice a year within a currency area in the Middle Ages. The exchange fee at re-coinage worked as a monetary tax for trade and inhabitants. The main purpose here is to set up a simple theory about short-lived coins, which has not been done before. It turns out that re-coinage works particularly well in relatively undeveloped economies. Such economies had a small volume of coins in circulation, which facilitates both re-minting and monitoring of a short-lived coinage system. Re-coinage had both positive and negative overlapping consequences: 1) a stable coinage with respect to weight and fineness, and no long-term inflation; 2) short-term disturbances in the velocity of money, price-levels and the volume of transactions; 3) the coins' function as a store of value deteriorated; and 4) inhibitions on trade, business and the division of labor. Debasement was the alternative method for collecting a monetary tax. It was less restrictive and had lower administrative costs for the coin issuer than re-coinage. Besides low monetization, the strong position of ecclesiastical coin issuers, who disliked manipulations of weights and fineness, was likely a factor in why re-coinage was preferred to debasement. However, the costs for society as a whole could be higher for secret debasements than routine calendar driven re-coinage, due to the high uncertainty.