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Mortgage rates are at their highest level in more than a decade. Home buyers are fighting back.

More borrowers are paying fees to cut their interest rates and making higher down payments to lower the amount they have to finance, lenders and real-estate agents say. People buying homes under construction are choosing to lock in today’s rates rather than risk even higher ones later.

And more home buyers are considering home loans that carry lower rates in their early years. Applications for adjustable-rate mortgages have doubled over the past three months, according to the Mortgage Bankers Association.