How early should I drive to avoid rush hour traffic?

I'll be driving from Austin to New Orleans early morning this Friday. I'm trying to time my departure from Austin (thinking of leaving around 3am, but it's somewhat flexible) so to avoid driving through Houston at a bad time. When does the morning rush hour traffic really amp up? I'll be most likely be taking I-10 all the way through. I know Houston traffic is bad, just hoping I can avoid the worst of it by planning ahead. Thanks so much!

EDIT: Thanks all for the advice! Here I was thinking I would try to be prepared and plan for Houston, when Louisiana could be the real problem…