Not sure why the hospital would suggest this, it's an old wives tale and doesn't have any effectiveness in easing constipation. I would suggest getting a second opinion.
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If you are referring to brown sugar, it isn't an old wives tale. Sugar based laxatives like the synthetic lactulose increase the water absorbed back into the stools, softening them. Brown sugar has the same effect. Health services and hospitals recommend it as does an emergency pediatrician I work with.
The thing to remember is if brown sugar/ lactulose is used, it's important to ensure baby is hydrated, as water lost is potentially dehydrating baby if used too often. Ensuring baby is hydrated is one way of ensuring constipation risk is reduced.
Prune juice is ok, but diluted 1:1 with water up to 1:3 with water depending on who you read.
Hmm, it is definately in the Pregnancy, Birth and parenting Information Book we got from the Hospital. And as per Stretcher bearers post above, our paed actually told us something similar when we were having issues with DD. I also remember him mentioning that a few years back one of the formula brands increased the sugar content specifically to reduce the incidence of constipation.