Yes, drop the grains and add fat to those lean meats! A little salmon and ribeye does more for the health of many people than a pound of dry, squeaky chicken breasts! Add a little heavy cream to berries or coffee, butter to veggies, etc etc. I feel best with at least 50% of my calories coming from fat, and constipation isn't an issue.
Consider adding in Magnesium Citrate caplets, though, as it is not only relaxing for your muscles but really gets things moving down below