I don't know if this is really a great way to do it but it works for me
and I end up with no bulk under the arms. I take a really long piece
of yarn/thread to sew the seams and start at the top shoulder. Pull
half the length of the yarn through and sew down one side to the under
arm. Go back and take the other half and sew down the other side to
the under arm. There should be two long lengths of yarn there now.
Take one to sew down the arm seam and the other to sew the side
seam. Basically using one piece of yarn to sew the side seam,
around the arm hole and the sleeve seam but starting it at the top
of the shoulder.
Not sure I explained that very well, sorry!