Hierarchical menu: How?

C++:
I create a menu:
    ICommandBarPopupPtr pPopupMenu = 0;
        pPopupMenu = m_pCmdBar->ActiveMenuBar->GetControls()->Add(xtpControlPopup, 0, _bstr_t("TEST"), -1, false);
        pPopupMenu->PutId(32000);
        pPopupMenuControls = pPopupMenu->GetCommandBar()->GetControls();

Add a menu item:
            pAction = pActions->Add(101, _bstr_t("New"), _bstr_t(""), _bstr_t(""), _bstr_t("TEST));

            pControl = pPopupMenuControls->Add(xtpControlButton,  101, "");

I create another menu (as above), and want to add this first menu to it.  I iterate over the CommandBar controls to find the control with this menuname/menuid (TEST/32000), and try to add it to the new menu:
          assert(xtpControlPopup == pCtrl->GetType());
          OutputDebugString(pCtrl->GetCaption()); OutputDebugString("\n");
          // This looks like the control -- popupMenu -- that I am looking for....
          pPopupMenuControls->AddControl(pCtrl);

Unfortunately, the TEST menu does not appear on the second menu I create.
What am I doing wrong?
TIA for any advice...