What if it only took you 10 times playing through a tune for you to memorize it? Would that interest you? Learning to play a new tune is a process. The problem is that if you start playing the tune quickly with a lot of bumps and snags, it will take you forever to learn and memorize the tune.
Playing the bagpipe is about precision, largely because we play all of our music by memory and, hopefully, with other people that are playing exactly the same thing at the same time. That being said, I have devised a process for developing a new tune that will not only help you learn it faster but improve your sight-reading at the same time.
As this is a process, I am going to list the sequence of practice steps:

1) Define and say the rhythm. You do this first because the main reason pipers don’t learn new tunes that are out of their comfort zone is because they don’t understand the rhythm. If that is a problem for you, I have some tools to help you learn and understand rhythm.
2) Say all of the melody notes (the notes with the stems down) out loud. When you can name them at a decent rate (1 per second) then you can go to step 3.
3) Finger all of the melody notes (position changes, not repeated notes) while naming them out loud. Start slowly so that you don’t make any mistakes. When you get to one note per second you can graduate to the next step.
4) Finger the tune including the ornamentation while saying them out loud. Again the goal is one movement per second.
5) Now you can stick the mouthpiece in your mouth and blow. The goal is to go from one melody note through the ornamentation to the next melody note position. You want to crawl through this step. The goal is to get from the beginning to the end of the tune without a mistake. That means that if you have to sit there on the melody note pondering the ornament coming up that is fine.
6) Step 5 was the first pass through the tune. If you didn’t make any mistakes the next time will be easier. Remember step 1, the rhythm? Because you have an idea how the rhythm goes, your tune will gradually take shape as you become more accustomed to the fingering through the repetitions.
Finally, playing a tune 10 times in a row won’t result in memorization if you play it 10 different ways. The goal is to play it exactly the same way 10 times in a row. The secret word here is patience!