As a result of monetary stabilization in Ukraine, inflation dropped from over 10,000 percent per annum in 1993 to around 40 percent per annum in 1996. Concurrently, the level of seignorage, or inflation tax revenue, dropped from 13 percent of gross domestic output to around 1 percent of output. This paper estimates a stock adjustment money demand function using quarterly data for the Ukrainian economy to answer two questions. What is the revenue maximizing rate of money growth? What is the seignorage loss due to monetary stabilization per se? The steady state revenue maximizing rate of money growth is found to be between 69 and 81 percent per quarter. The loss in inflation tax revenue is found to be on the order of 2 percent of output--a relatively small fraction of the total loss in seignorage of some 13 percent of output. Consequently, calls for a return to previous hyper inflationary rates of money growth in order to reproduce earlier levels of seignorage revue are seen as misguided.