One Bitcoin can be compared with one ounce gold coin, so we could use 1/2, 1/4, 1/10 BTC etc...
Below that, there are other weight unit, like carat (bitcarat) and grain (bitgrain)
I suggest that one carat bitcoin (bitcarat) = 1/1000 bitcoin, this sounds luxury enough

And one grain bitcoin (bitgrain) = 100 satoshi = 1/1,000,000 bitcoin