Here are some that I use and recommend. I have no financial ties to them. I buy them from Amazon, Vitamin Shoppe, Lucky Vitamin, and Vitacost- depending on what's on sale. I'm sure there are others but this my research.
The kicker is that some of these same companies when you change to another dose say a greater IU of Vitamin D or Kelp they add soybean oil, soy lecithin, or olive oil so read the labels carefully!
Also the Rainbow Light Organic Men's formula has a trivial amount of iodine 55 mcg/4 capsules whereas the Womens' has 75 mcg/4 capsules and Prenatal has 150 mcg/4 capsules.
1) Rainbow Light Certified Organic Womens, Mens, and Prenatal formulas/4 capsules daily are
Free Of: Artificial colors, flavors, sweeteners, preservatives, sugar, lactose, gluten, yeast, milk, eggs, soy, nuts, fish/shellfish and wheat.
2) Citracal Plus 2 tablets/day includes Vitamin D3, zinc, magnesium, copper, etc.
3) NOW Zinc Picolinate 50 mg/tablet
Free of: sugar, salt, yeast, wheat, gluten, corn, soy, milk, egg or preservatives.
4) NOW 150 mcg Kelp (Iodine)/tablet
Contains no: sugar, salt, starch, yeast, wheat, gluten, corn, soy, milk, egg, shellfish or preservatives.
5) Carlson Cod Liver Oil/Fish Oil (both Lemon and Regular Flavor) liquids and capsules
EXCEPT Very Finest Fish Oil SOFTGELS or Fish Oil Multi
No gluten, corn, milk, soy, yeast, sugar, salt, preservatives
6) Nature's Bounty D3 400 IU/tablet
NO artificial color, flavor, sweetener, preservatives, sugar, milk, lactose, soy, gluten, wheat, yeast, fish, sodium
7) KAL Magnesium Orotate 200 mg/2 tablets daily
Does Not Contain: Yeast, wheat, corn, milk, egg, soy, glutens, animal derivatives, sugar, artificial colors, starch or preservatives.