When I open a new dialog box modelessly in my dialog based app, it is
unresponsive:  it can't be moved and the buttons don't respond, though
the controls can be updated.

The new dialog is opened in the traditional way: created on the heap,
->Create(), and eventually destroyed with ->DestroyWindow();

I've also tried opening my main dialog modelessly, and various
combinations of EnableWindow, SetFocus without success.

Any ideas?