A breast pump sat on the passenger seat of her gray Honda Accord. Ms. Van Son unscrewed the pump’s handle and shoved it into her bra.

Retracing her steps, she strolled back into the prison, past an indifferent guard, and hid the contraband on a shelf in the pharmacy. Over the next two nights, she sneaked in every piece of the pump, save for one. Ms. Van Son’s breasts weren’t big enough to conceal the funnel, so she enlisted a better-endowed colleague to shuttle it in for her.

Other women who worked at the prison took part in similar smuggling schemes. It was necessary, they said, because Deerfield, a state prison in the town of Capron, didn’t allow them to bring breast pumps into their work space, inside the security perimeter.

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That situation, where producing breast milk at work is unfeasible, is common among American employers — even though failing to provide hourly workers with break time and a private place to pump is often a violation of federal law. There are health consequences for potentially millions of families.

There is consensus among doctors that breast-feeding tends to make both mothers and their children healthier. Controlling for socioeconomic factors, studies find that babies who consume breast milk are at lower risk of sudden infant death syndrome, infections, allergies, asthma, childhood diabetes and two types of leukemia. Mothers who breast-feed or pump are at lower risk for breast and ovarian cancers, diabetes and hypertension.