From what I have read, FHA mortgage loans are backed by / insured by the government, so how are lenders also allowed to require / charge you for PMI (Private Mortgage Insurance) on FHA loans?

I have read PMI occurs when less than 20% is put down on a house.

If you are doing a FHA loan, where the down payment requirement is only 3-3.5%, is PMI still a factor?

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I have a 15 year FHA loan that origninated June 2 2008. I had a 10% downpayment and had upfront PMI tacked on to the loan. I would now like to refinance to a 30 year conventional loan with 20% down. Will a percentage of my current PMI be removed or have the laws changed?