You're going to get a couple of wet taps during fellowship. Don't sweat it. Since fellowship, I've had just one wet tap in my entire career by using the fellow technique:
1) Avoid injecting at levels whereby there is severe stenosis.
2) Stay near midline, but make sure you don't cross midline --> If you switched to CLO, but had to travel quite some distance to get to the VILL, you may have accidentally crossed midline, so don't be afraid to go back to AP to make sure you haven't crossed, then return to CLO, and proceed.
3) Make sure you have a true CLO. Dogma is 45 degrees for lumbar, 45-55 for cervical, but every patient is different. The lamina should be crisp.
4) Use a glass LOR syringe (I've found these are much more sensitive to pressure loss)
5) Advance under CONTINUOUS pressure with your LOR syringe. Not only is this more sensitive, but some believe that the pressurized water jet pushes the dura away the instant you enter the epidural space, thus protecting the dura from puncture.
6) When you advance, make sure your fingers grasp the needle at the skin, with the side of your palm/wrist resting/posting on the patient's back (this is for maximal control). Advancement should be made by "rolling" your thumb and index fingers (the fingers grasping the needle shaft). Advancement should not require anything but your fingers. If you're using your hand/wrist (or anything else), your advancements will be too coarse, and uncontrolled. Once you are at/near the VILL, advancements should be made in 1 mm (or less) increments, again, under continuous pressure.
7) Pay special attention to tissue feel. Once you get to that "connective tissue" feel, switch to LOR even if you aren't yet at the VILL.
With this, you shall not wet tap (much).