Thought of that, but it is controversial. Disme (the spelling on the first types) may have the same root as the "decime" of the French revolution and be a denomination. However, it may also be a nickname, much like penny, nickel, quarter, 2 bits, and half are nicknames, even though they may refer to a British coin or Spanish peso/reales coins.
As a comfort, I offer that many US tax tokens are denominated in mils, so that in the end the US did have multiple sub-units.
Peter