What version of electrum? How much are you sending?
1.9.8 I've tried it with different amounts. Last normal sized transaction I did was ~0.3 and it wanted 0.0004. Maybe if I set the default to 0.0001 it would have taken it as a 0.0002 transaction, but I'm not sure.
I'll keep testing it out seeing if I can find ways to send some tx's with lower fees. I guess some of my transactions are just too many kbs.
Open /lib/bitcoin.py in electrum's install folder. (you can't do this with the standalone version)
Search for
Change that number from 10000 to 1000 (this is the new minimum fee for 0.9.0 and beyond.)
Then after you save that file, restart electrum, then go into preferences and set the default fee to 0.00001 BTC (or 0.01 mBTC) and save.
A little more than half of miners use 0.9.0 and beyond, so you might have to wait 20 minutes instead of 10 minutes for your first confirmation.
WARNING: Setting that number in bitcoin.py to 0 is a bad idea, recently 0 fee transactions that require fees can take days or even weeks to confirm.