The shallowest freezer really depends on a few things.
First of all, do you mind having a compact refrigerator? If so, no worries there are plenty of refrigerators that fall into this category.
But if you want to get a full size refrigerator then you'll need to look at counter depth refrigerators. They are around 30" deep and are made to match the depth of your counter (hence the name counter depth).
