In Tall, Tall, Mountain, there is a warp that makes it easy to get to the cannon. In the area with all of the mushrooms, you will see two tiny mushrooms that are next to each other. Jump to the second tiny mushroom, and you will warp to a hidden area below the mountain. From there you can head to the cannon. You can also warp from the hidden area to the mushroom if you decide not to use the cannon.