YES Enclose That Checkout
As a Director of Ecommerce I came to think of checkout as similar to a plane landing. When a plane is landing its wheels are down, flaps set and they are coming in UNLESS there is a distraction or a danger. 

Checking out should be like landing a plane - clear, well mapped and without distractions or dangers. Enclosing the checkout reduces distractions. 

You worked so hard to get your customers into a checkout process you should ENCLOSE the process by reducing or eliminating upsale, navigation and other distractions and this post shows you how.