How to place combobox in the tab's title?

Question

Is it possible to show combobox (better if it will be extjs combo) in the tab's title?

I have created an example on jsfiddle but there are such issues:
1. It is not possible to show combo's options list (mouse click don't work)
2. Tab's height is incorrect (I guess this can be fixed by applying height to the combo).

Sample code:

new Ext.TabPanel({
    renderTo: 'tab-with-combo',
    activeTab: 0,
    items:[
        {
            title: 'First tab ' +
                '<select>' +
                    '<option>Option 1</option>' +
                    '<option>Option 2</option>' +
                '</select>'},
        {title: 'Second tab'}
    ]
});

Answer 1

Thanks for @Alexander.Berg answer, this works correctly (example is here):

var comboId = Ext.id();
new Ext.TabPanel({
    cls: 'tab-panel-with-combo',
    renderTo: 'tab-with-combo',
    activeTab: 0,
    items:[
        {
            title: '<div class="tab-title" style="float: left; padding-right: 5px;">First tab with a long name</div> ' +
                   '<div style="float: right;" id="' + comboId + '" ></div>',
            closable: true,
            html: 'Content of the first tab'
        },
        {
            title: '<div class="tab-title">Second tab</div>',
            closable: true,
            html: 'Content of the second tab'
        }
    ],
    listeners: {
        afterrender: function() {
            var store = new Ext.data.ArrayStore({
                fields: ['abbr', 'case_name'],
                data : [
                    ['one',   'Case #1'],
                    ['two',   'Case #2'],
                    ['three', 'Case #3']
                ]
            });

            new Ext.form.ComboBox({
                store: store,
                displayField:'case_name',
                editable: false,
                typeAhead: false,
                selectOnFocus:false,
                mode: 'local',
                forceSelection: true,
                triggerAction: 'all',
                emptyText:'Select a case...',
                renderTo: comboId
            });
        }
    }
});