How many states allow counting of absentee ballots before election day?

Sorry for the quick-hit diary, but I have a question for the Swing State Project community based on a story the Iowa Voters Blog brought to my attention.

On Tuesday the Iowa House approved a law that would allow absentee ballots to be counted before election day. (Click here to read the text of HF 670.)

Iowa Voters writes in a satirical style but raises a lot of valid concerns about this bill:

Don’t worry about this affecting the election by giving one side a warning that the results may be close. Don’t worry-it will be illegal to leak this information even though some highly political people at the courthouse will know the information on the absentee results. Don’t worry even if the county auditor himself is in a tight re-election race. Having his staff counting the ballots on Monday won’t allow him to be warned about his imminent defeat on Tuesday. Don’t think that the people who went to jail in Ohio for rigging the recount in 2004 have any cousins in Iowa election departments.

I can’t see any public interest served by this bill. Even though early voting has grown in Iowa, with about a third of the electorate casting early ballots last fall, we still got our election results promptly. It’s not as if it took days for those officials to count the absentee ballots.

Are there any other states that allow the practice of counting absentee ballots before election day? Am I crazy, or is this bill a solution in search of a problem?