class MyControl : TextBox
   {
       uint foo;

       public uint Foo {
           get {
               return foo;
           }
           set {
               foo = value;
           }
       }
   }

When I create an instance of this control with VS.NET's form designer, it
complains that 'Foo' isn't a CLS-compliant type and that it can't create
code that sets it.

How can I fix this?  And is how to fix this documented anywhere?

Creating a simple control that works with the form designer seems to be a
case of guessing how to do things and then using trial and error.  The MSDN
documentation is apparently useless here.