Next code creates window with thin border and fixed size:

 
#include <QtGui/QApplication>
#include <QWidget>

int main( int argc, char *argv[] )
{
    QApplication a(argc, argv);
    QWidget w;
    w.setWindowFlags( Qt::Window | Qt::CustomizeWindowHint );
    w.setFixedSize( 300, 200 );
    w.show();
    return a.exec();
}

This window is without title bar, but is is draggable by the top border. Window without title bar, should not be dragable.

Note that such windows without fixed size working OK - dragging will change window size, as expected.