I'm lottery mining with a BitAxe Supra on the solo pool, and I noticed something strange on startup.

The initial difficulty after a connection is set to 10000. This takes a little while for a BitAxe to find a share, and submits. After a few shares, the pool sets the difficulty down to something around ~500, and the BitAxe starts submitting shares on this difficulty after that, but the first few shares are not accepted due to 'Above target'. This takes about 40 seconds. After that, the shares are suddenly accepted.

There are some logs with stratum communication on https://github.com/skot/ESP-Miner/issues/212.