Kendall Jack was dismayed when her health plan stopped covering her migraine drug Treximet earlier this year. To buy a pack at the pharmacy would cost $750, compared with a $20 copay when the drug was covered.

“Nothing’s worth $750 for nine pills,” she said. “It’s cruel.”

Instead, the 50-year-old stay-at-home mother from Memphis, Tenn., takes Treximet’s two active ingredients—sumatriptan and naproxen—as separate pills. For these two generic drugs, her copay is zero.

A spokesman for Pernix Therapeutics Holdings Inc., which sells Treximet, said the drug addressed an unmet need among migraine sufferers by combining sumatriptan and naproxen into a single tablet. He also said Mrs. Jack could get a pack of Treximet for $20 by contacting the company directly.

Treximet is just one of many drugs whose active ingredients are generic drugs that can be purchased separately at a fraction of the cost. Others include acne cream Acanya, Duexis for rheumatoid pain and weight-loss pill Qsymia, according to data compiled for The Wall Street Journal by GoodRx, a group that compares pharmacy prices for prescription drugs.

A spokesman for Valeant Pharmaceuticals International Inc., which makes Acanya, said doctors could prescribe whichever medication they believe is most appropriate for their patients. Valeant is one drugmaker that has come under fire amid a broader eruption of public anger at drug companies for sharp price increases in recent years.

A spokesman for Horizon Pharma PLC, maker of Duexis, said combining its constituents made it easier for patients to stick with their drug regimen. Mark Oki, chief financial officer of Vivus Inc., which makes Qsymia, declined to comment.

For Treximet, a box of nine tablets costs $728.67, according to Truven Health Analytics. Insurers and employers typically pay less than this so-called list price as a result of behind-the-scenes discounts: the average actual cost for a box of Treximet is about $353, according to an analysis of company-reported sales and prescription data from IMS, a health-care data company. To buy its two constituents, sumatriptan and naproxen, would cost around $19, according to GoodRx.

There is no evidence that Treximet tackles migraines any better than a two-pill regimen of sumatriptan plus naproxen. The two clinical trials that led to its approval pitted it against sumatriptan alone, naproxen alone and placebo. Those trials were jointly conducted by GlaxoSmithKline GSK 0.47% PLC and Pozen Inc., now called Aralez Pharmaceuticals PLC. Glaxo transferred the rights for Treximet to Pernix in 2014.

Some patients avoid paying the full price for Treximet because the cost is partly covered by their health plans. But those whose plans don’t cover Treximet face the pharmacy price, which often exceeds the list price.

Pernix and others said they issued coupons to keep patient copays low in some cases. Even so, patients likely will end up paying for it indirectly. “Premiums go up, or it’s passed on to employers,” said Michael Rea, chief executive of Rx Savings Solutions, a software company that helps employers and health plans lower their prescription costs by pointing patients to cheaper alternatives. “It all comes out of the same bucket.”

In some cases, combining two or more drugs into a single pill has benefits, such as added convenience, said Bernstein analyst Ronny Gal. The problem: There is no agreed-upon process for assigning a fair value to those benefits.

“This is one more example of the inefficiency of the U.S. health-care system,” he said. Mrs. Jack is a case in point: She would be willing to pay a premium price for Treximet, which she finds more effective than two separate pills, but not $750 more.

What’s more, patients and their doctors often have no idea that a cheaper alternative exists. “Americans shop [around] for everything in their lives, except medications,” said Mr. Rea of Rx Savings Solutions. “They don’t know how.”

“Understanding the price of medication with the myriad of health plans offered in the U.S. is extremely complicated,” said Anand Rajani, a pediatrician based in Fresno, Calif., who owns a small stake in closely held Rx Savings Solutions. “Physicians are totally unaware” of the price.

To complicate matters further, some combination drugs use slightly different doses than are easily available to buy separately in the pharmacy. A single pill of Treximet contains 85 milligrams of sumatriptan and 500 milligrams of naproxen. When sold separately, sumatriptan comes in pills of 50 milligrams or 100 milligrams, making direct substitution difficult.

Sharon Orrange, an internal-medicine doctor at Keck Medical Center of the University of Southern California, said she had switched many patients to generics from branded drugs which, like Treximet, comprise two generic constituents. She also works as a consultant for GoodRx on which branded combination drugs can be substituted with cheaper generics.

For many of these patients, the savings are substantial, she said: “I have patients who can use the money [saved] to join a gym, or take a trip they couldn’t take before.”

Write to Denise Roland at Denise.Roland@wsj.com