If you tend to come too much from the inside or hit fat shots at times, try this simple change.
Set-up as you would normally do using the simple swing method. If you set-up correctly, your head should be behind the ball and tilted slightly to the right (rh person) because your spine is tilted to the right. Viewing the ball and your target line from this position can feel awkward and tends to make you swing too far from the inside.
Try this simple move. Tilt your head to the left (rh person) until your eyes are parallel to the target line (it's not a big move.) Move nothing else, your head should still remain behind the ball. Make your normal swing.
Using this method, my view of the ball and target line feels more natural. I tend not to swing from the inside as before and my shot dispersion is much tighter. I just feel more confident.
This simple set-up change made a world of difference for me. I hope others will give it a try.
Your rather simple sounding tip really does work. I would definitely recommend it to Symple Swingers.
Just straightening the head slightly like you suggest can really help you keep the club on-plane. The majority of students I see take the club back too much inside (meaning under the proper swing plane).
Taking the club back under the swing plane will almost always result in a least a draw and maybe a hook. If you draw or hook more than you like take a good look at this tip.
Remember the correct swing plane is defined by three points. Your left shoulder, the ball and the target.