I do the "Push out" method (if it is a method) as well. Pipe you first circle the angle your tip into the inside of that bead of icing and add more icing until you flood your cookie...it will push out your initial piped circle to where you want it to be. So, the haphazard initial piped circle is not even visible you have a pretty concentric circle. Hopefully I explained that well.
I am a leftie and I go counter clockwise, but I make sure I am piping about an inch off my cookie and it drops so much better.