From IFBB Pro Fouad Abiad:
If you’re looking for good protein sources and you stay away from red meat because of fats, check out the eye of round cuts. These cuts are the leanest of all the red meat. Depending on what book you read or website you will find they only have 3.5g of fat per 4oz portion. Thats leaner than a chicken breast!
Like everything there is a bad side to this. The fact that there is so little fat in them makes them tougher to eat and chewier. The solution I came up with for this problem was getting my meat ground up. Call your butcher and have them grind up your portion of round steak for you then it basically feels like your eating ground beef! But much healthier!!