I'm thinking of switching to a low-iron formula because my baby is constipated. Is that a good idea?

A study was done about whether iron in formula causes constipation in babies. Half were given low iron, the rest were fed regular -- not knowing which was which -- and the rate of constipation was the same in both groups. So it doesnt really make a difference and ultimately the iron is very important for growing babies. The constipation might be formula-related. Allergies to some of the proteins in the formula could cause the discomfort. Sometimes switching to another brand or even soy will help. Source: http://www.parents.com/baby/feeding/formula/constipation/

My son is on 100% formula and was terribly constipated when he was about 3 months old. Since he wasn't allergic to the brand that I was giving him, I didn't see the need to switch brands. Instead, I mixed gripe water into his feeding and gradually, he started pooping regularly.

thanks