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Is threatening to close the account a good way to negotiate with the bank?
Take your business elsewhere, where the products and services are priced at a level you agree to pay.  This does two things.  First, you end a bad business relationship.  Why bad?  Because you're not happy with the deal.  Second, it sends an unambiguous signal to the losing bank that you were unhappy with their service.  If they offer an exit survey, complete it, and be sure to tell them what made you unhappy with their service. In a free market economy, if consumers all take their business where the terms are favorable, supply and demand would force the banks to compete for consumers' business.