TRENTON, N.J. — If brand-name prescription medicines cost you as little as generic pills, which would you choose? A few drug makers are betting Americans will stick with the name they know.

They have begun offering US patients coupons to reduce copayments on brand-name medicines and compete with new generic versions of the drugs. The medicines include staples in the American medicine cabinet — cholesterol fighter Lipitor, blood thinner Plavix, and blood pressure drug Diovan — along with drugs for depression and breast cancer.

Pfizer Inc. tested the new trend last year and now offers copay coupons that can bring insured patients six of its medicines for as little as $4 a month each. That includes Lipitor, which was taken by more than 3.5 million Americans until generic competition arrived last Nov. 30.

Experts predict more drug makers will do the same for some of their big sellers, as the companies weather big revenue drops from an unprecedented wave of top-selling drugs whose patents are expiring. The trend is the latest attempt by drug makers to hold onto business at a time when they are increasingly under siege. Drug companies including Pfizer, Merck & Co., and Bristol Myers-Squibb Co. are squeezed by rising research costs, the weak global economy, and pressure from Europe, China, and elsewhere to reduce drug prices.

So, they are trying a new tactic to temporarily slow the loss of billions of dollars in sales to new generic competition.

‘On a big drug, every day that you can delay the sales drop is a happy day at the drug company.’

‘‘On a big drug, every day that you can delay the sales drop is a happy day at the drug company,’’ says Erik Gordon, a professor at the University of Michigan’s Ross School of Business who follows the drug industry.

Developing drugs is very expensive. It requires up to a decade of laboratory research and then patient testing, costing $1 billion or more, to win government approval to sell a drug. In return, the drug’s maker gets the exclusive right to sell the drug for about 10 to 15 years, until the patent expires. That allows the companies to recoup those costs and hopefully turn a profit. After that, generic copycats sold by other companies flood the market, costing just a fraction of the brand-name drug’s price, even though they are chemically identical.

Often, one generic drug maker has the exclusive right to sell its copycat version for the first six months after the branded drug’s patent expires. In those cases, the generic’s price is only about 25 percent lower than for the branded drug. Other times, there are multiple generics right away. Either way, once several generics are on sale, their prices usually plummet to about 90 percent below the brand-name price. Nearly all patients then switch to a generic.