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I would say that it should take around 30 days for the FHA streamline refinance. Since you have all your information together from the last lender you should be able to easily give that information to another lender if you wish to do so. [self promotion deleted by Zillow moderator.
A refinance requires no missed payments for at least one or two years, and a minimum credit score, typically at least in the mid- to high-600s. Sufficient time must elapse between the modification and your application to meet most of the minimum eligibility requirements for a refinance.