Double Jump Cancelling

Double Jump Cancelling (also known as DJC) is a technique that involves using an attack or Air Dodge during a midair jump to cancel its upward acceleration. This allows the character to perform very short, low midair jumps while performing an attack. Only characters with unique double jumps may perform a DJC, with only four characters who can perform this technique: Yoshi, Ness, Lucas, and Mewtwo.

How to Perform
The basic way to perform the DJC from the ground is by tapping Jump, Jump and then an attack in quick succession. For example, Ness can do Jump, Jump, A to perform a DJC Nair. If performed correctly, Ness should do the Nair while returning to the ground much earlier than if done from a short hop.

Yoshi
Yoshi can use DJC's to perform low Nairs and Uairs, and he can take advantage of the Super Armor on his double jump to blow through some attacks just before his own.

Ness
Ness is possibly the best user of DJC currently due to his quick aerial strikes. His Uair deals strong damage aand knockback, carries good shield stun, and has a very quick startup, making it an ideal DJC move. Not only that, bbut by L-cancelling it, Ness can perform combos starting from it. Fair and Nair also make good DJC aerials due to their quick startup times and favorable hitboxes. Dair also works well from a bit higher from the ground and can combo into other moves on stage.

Lucas
Lucas has a very similar DJC to Ness. Because Lucas's moves are slower than Ness's in general and don't have the same angles, the DJC has quite a different application for Lucas. Nair can be used as a DJC aerial, and its multiple hits can make it a flexible offensive move. It even has some combo potential when L-cancelled. Fair and Dair can be used a bit higher from the ground than Nair, creating a sort of "Triangle Jump" attack. This has offensive and defensive potential. especially when used with Fair. The Uair is at least as effective as Nair, since, like Ness's, it's quick and potent. It has less knockback than Ness's Uair does, making it better for combos. However, the hitbox is slightly narrower, and the move's startup is a frame or two longer, so it's more difficult to use.

Mewtwo
Mewtwo can utilize DJCs for his faster aerials, but overall, he doesn't get a lot of mileage from the technique. His Nair is an obvious candidate, posessing a fairly large hit area and fast startup. Fair is effective, with a fast startup, good KO power, and good shield stun, only held back by its tiny hitbox. Uair is also a candidate, but situational due to its somewhat slow startup speed. In most situations, Nair is the most practical, but because Nair has a landing hitbox, it can't be used for combos. This makes Fair the only reliable one, and it requires precise spacing.