Here are some tips to avoid ‘side to side’ vibrato motions. First and foremost, make sure you are holding the violin with your head only. Lots of bad habits, and inhibited movement in vibrato is often caused by a violin hand helping hold the violin. So, practice sirens and letting go the left hand to be sure your shoulder pad and chin rest are working for you and that you’re holding your violin firmly and confidently with head only. Once sure of this, bring the violin hand into position, then pull it in and up, above the violin neck, so that your wrist is gently touching the violin neck near first position. Wave the hand toward your nose and away to achieve a vibrato motion that is starting at the wrist, and is moving in the correct direction – toward your nose, away from your nose. When you’re confident in this, move this relaxed, waving hand back to playing position, still waving in the correct motion, but only touch the violin thumb to the neck of the violin in its usual spot. The rest of your hand is still waving from the wrist toward you and away, staying slow and relaxed. Place a tissue at the base of your first finger and pretend to polish the neck of your violin with this waving motion. You hand is stabilized by the thumb. While doing this, focus your mind on the tip of your third finger as it gets gradually, slowly closer to the A string. Be sure you’re violin is still secure with head and that you’re violin hand is waving at you from the wrist joint. Place the third finger on A very lightly, allowing it to slide naturally up and down on the string with the rest of your waving hand. Make the waving motion smaller and smaller until the fingertip finds A3 (aka D) position. The hand now touches the violin in two places only, the thumb and the fingertip. The tissue separates the base of the first finger from the violin neck as you maintain waving, smaller now. Note the third finger joint above the tip is loose and movable. Keep your violin elbow well under the violin. Most people have trouble keeping the base of the first finger from sticking. This signifies that you are holding the violin with your hand a little. Re-evaluate the head position and make sure the violin is being held only by the head. A hand that has to hold the violin will not perform a fluid vibrato and will have trouble shifting, too. Good luck!