Please look this example:
select { width:192px; padding:2px; border:none; background:url(http://imgur.com/MJyZM.png) 0 0 no-repeat; -webkit-appearance: none; }
abcdefg 1234567 abcdefg
Not tested on firefox but it seems -webkit-appearance: none; disables specific behaviours webkit can apply.
-webkit-appearance: none;