Voter ID Laws: What's More Important?

I was just on a blog discussing the wave of "voter ID" laws that Republicans have proposed in numerous states, and a question came up that I'd like your opinion on.

Let me preface this by observing that in the 2008 elections there were less than 100 confirmed cases of people who were not entitled to vote managing to cast a vote, out of about 150 million votes cast. That's literally less than one in a million. On the other hand, it turns out that many thousands of people who actually were entitled to vote were not permitted to vote because someone thought their ID wasn't sufficient, or because they were mistaken for someone with a similar name who really wasn't entitled to vote, etc. In 2000 Katherine Harris in Florida knocked over 8,000 people entitled to vote off the voter rolls because their names were similar to the names of people who were convicted of felonies in Texas. There was no background check, no verification of social security numbers, nothing. If "John Smith" was convicted of a felony in Texas and you happened to be a Floridian named "John Smith" there's a good chance you weren't allowed to vote.

So the question is this: Is it worth preventing one ineligible voter from voting if the cost of doing so is preventing 10,000 eligible voters from voting?