Allmenus.com yesterday launched a new feature that somewhat solves this issue. In the shopping cart, we have text reading 'Discount Code' with a link 'Apply'. If you click the link, we reveal an input box with a button to submit a coupon code.

I believe that by removing the text box, less visual attention is stressed to go out and find a coupon. If a customer has come to our site with the prior intention of redeeming a coupon, I believe they'll navigate our interface without a problem.

See what i'm talking about, just add an item from the menu to meet the order minimum to see the text appear:

http://www.allmenus.com/ny/new-york/280265-yorganic/menu/

Sidenote: Yes, we'll test the lingo to determine what preforms the best and monitor campaign results for changes in usage patterns.