Constrain QGraphicsItem movement with mouseMoveEvent

I am attempting to properly constrain the movement of a QGraphicsItem (specifically QGraphicsRectItem) without changing the native behavior to function as a scrollbar on the X-axis.

I tried overriding the mouseMoveEvent function, but then I need to re-write the behavior for the rectangle in both the X and Y directions. At best, I can get the rectangle to snap to a single position with the mouse. (Here the rectangle will snap so the mouse holds it at the midpoint):

void SegmentItem::mouseMoveEvent(QGraphicsSceneMouseEvent *event)
{
  setY(0);
  setX(event->scenePos().x() - boundingRect().width()/2);
}

I'm looking at itemChange right now, as described here, but it looks a little unwieldy and not exactly elegant.

Is there a way to just constrain the y-axis movement? (I will also need to create endstops for the scrollbar, but later.)