How do I controll clipping with non-opaque graphics-item's in Qt?

Question

I have a bunch of QGraphicsSvgItem's in a QGraphicsScene that are drawn connected by QGraphicsLineItem's. This show's a graph of a tree-structure.

What I want to do is provide a feature where everything but a selected sub-tree becomes transparent. A kind of "highlight this sub-tree" feature. That part was easy, but the results are ugly because now the lines can be seen through the semi-transparent svg's.

I am looking for some way to still clip other QGraphicsItem's in the scene to the svg item's, giving the effect that the svg's are semi-transparent windows to the background.

I know this code does not use svg's but I figure you can replace that yourself if you are so inclined.

int main(int argc, char *argv[]) {
    QApplication app(argc, argv);
    QGraphicsScene scene;
    for( int i = 0; i < 10; ++i ) {
        QGraphicsLineItem* line = new QGraphicsLineItem;
        line->setLine( i * 25.0 + 1.0, 0, i * 25.0 + 23.0, 0 );
        scene.addItem( line );
    }

    for( int i = 0; i < 11; ++i ) {
        QGraphicsEllipseItem* ellipse = new QGraphicsEllipseItem;
        ellipse->setRect( (i * 25.0) - 9.0, -9.0, 18.0, 18.0f );
        ellipse->setBrush( QBrush( Qt::green, Qt::SolidPattern ) );
        ellipse->setOpacity( 0.5 );
        scene.addItem( ellipse );
    }
    QGraphicsView view( &scene );
    view.show();
    return app.exec();
}

I would like the line's to not be seen behind the circle's. I have tried fiddling with the depth-buffer and the stencil buffer using opengl rendering to no avail.

How do I get the QGraphicsSvgItem's (or QGraphicsEllipseItem's in the example code) to still clip the lines even though they are semi-transparent?