Prefabs not showing up in the object browser

I've got different bullet casing prefabs in my game - different meshes, sounds, physics setup, etc. Each one has a `Case` MonoBehaviour attached to it. When setting up my guns, I can tell each gun which bullet casing it should spit out by wiring it up in the inspector.

If I drag and drop the bullet casing prefab into the object field, it works fine.

If I hit the little circle next to the object field to bring up the 'Select Case' window, the window appears but it doesn't list any of my prefabs on the Assets tab. 'None' is the only option.

What gives? Shouldn't all my prefabs with 'Case' behaviors attached show up in that list?

Edit: For completeness, here's the line in my custom inspector that produces the object field:

Target.BulletCasing = (Case) EditorGUILayout.ObjectField("Bullet casing", Target.BulletCasing, typeof (Case));

If your Drag and drop variable is listed as a transform then it will only look for those not prefabs. What is it listed as?