Research published in the British Medical Journal suggests that babies born even slightly prematurely have a greater risk of health problems in infancy than those born at the optimum 39 weeks.
Researchers studied a group of 14,000 children born in Britain 10 years ago.
Pregnancies are considered full term from the 37th week.
The researchers say babies formed before 39 weeks had a slightly higher risk of developing illnesses such as asthma.
However, the BBC reports the authors stress that parents should not worry about what is a modest chance of extra illness.
They say their work should be used to question the level of healthcare support and monitoring given to these families.