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The 0.3.21 release (I hope to have a release candidate available today) will support full-precision values-- you will be able to send 1.00123456 BTC, if you like.
Sending less than 0.01 BTC still requires a 0.01 BTC fee, though. Changing that to "sending less than 0.01 BTC requires a 0.001 BTC fee" might be worth thinking about, but I think there are higher priorities on the core bitcoin TODO list.