My theory, and I;ve never heard this anywhere so don't belive it yet - but are you eating enough?> NO, you are eating less, to lose weight right>
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So I think that the body "holds on" to get what more it can from it. The extra calories in ice cream help convince it.
I found that eating a pudding I make [but is not "healthy"] helps me go too. And like you, I eat a ton of veggies and other good "bowel foods", but still have some constipation troubles.