I have cooked, for at least the last ten years, my about-five pound eye round roast beef according to Barbara Kalfa's method: cook at 500 degrees for every pound of meat for 5 minutes, turn off the oven, DON'T PEEK, and serve two hours later. It comes out medium rare every time.
Hudson Valley Kathleen

If I'm thinking of the right cut, there's almost no fat on the eye round, therefore less flavor. Maybe wrap it in some pancetta or bacon to give it a little oomph. Also, definitely don't over cook that cut, or you'll be chewing for days.

The eye round was originally attached to the bottom round to make what they call a goose neck. So, you can treat the cuts the same. There is no fat on the eye round and tends to not have much flavour, but slow cook and keep rare, so it does not get too tough. If you like well done, then braise it very slowly with lots of root veggies, herbs, mushrooms and a couple of anchovy fillets mashed up for umami. Use wine or a good Belgium ale for the liquid.

I found good resource online direct from CI. I thought I couldn't view it without a subscription, but found that if I waited it comes up. Seems they hate the bottom round and find the eye of round a tad superior at best. lol. I'll print this out for future reference.
http://www.cooksillustrated.com/images/document/howto/ND02_BeefRoasts.pdf

Hi, while I don't use bottom round so can give you a comparison I have been getting deals on eye of round lately. Ifound unevenness in the tenderness until I did some research and found the Cook's Illustrated low heat method. This made all the difference. I made a modified version with great success. Here is a discussion about it.
http://chowhound.chow.com/topics/608907

This is also the time you may want to break out the slow cooker.
http://www.food.com/recipe/kittencals-slow-cooker-eye-of-round-roast-with-gravy-204976