The debate over formula samples isn’t about whether breast-feeding is healthier. Even formula companies acknowledge that “breast milk is the gold standard; it’s the best for babies,” said Christopher Perille, a spokesman for Mead Johnson, which makes Enfamil formula.

Breast-feeding decreases babies’ risk of ear infections, diarrhea, asthma and other diseases, and may reduce risk of obesity and slightly improve I.Q., experts say. The question is whether samples tempt mothers who could breast-feed exclusively for the recommended six months to use formula when they’re exhausted or discouraged if nursing proves difficult. The C.D.C., the World Health Organization and breast-feeding advocates say samples turn hospitals into formula sales agents and imply that hospitals think formula is as healthy as breast-feeding. Health experts warn that even small amounts of formula dilute breast-feeding’s benefits by altering intestinal micro-organisms and decreasing breast milk supply, since women produce less when babies nurse less. They say that while some women face serious breast-feeding challenges, more could nurse longer with greater support, and that formula samples can weaken that support system.

“We’re not anti-formula,” said Dr. Melissa Bartick, a founder of Ban the Bags, a breast-feeding advocacy group, which reports that one-fifth of the country’s nearly 3,300 birthing programs have taken more comprehensive steps of banning samples and logo-emblazoned bags for all mothers. “If a woman makes an informed choice to formula-feed, the hospital should provide that formula. But hospitals shouldn’t be marketing it.”

The industry and some mothers say samples provide a healthy alternative and offer relief if nursing causes pain, fatigue or frustration. They disagree that samples can shake the resolve to breast-feed exclusively.

“Babies grow fine on it,” said Mardi Mountford, executive vice president of the International Formula Council, who breast-fed her baby exclusively. “And moms tell us they like getting the samples.”