Zap Jump

Zap Jumping is an advanced technique that doubles the height of Lucas's second jump. It was discovered by Christopher Daniel Winans.

Execution
To execute this boost, the player must use PK Fire within one frame of his double jump, essentially pressing them at virtually the same time (one sixtieth of a second delay). Lucas's double jump propels him with an upward force (like most characters), but for some reason the ascent is hindered by a downward force right after this, which is apparently negated by the side special move.

The bolt of fire is released about halfway through the jump, and combined with B-sticking and Magnet Pull, Zap Jumping allows for an impressive recovery. Due to the obscure nature of jumping immediately after a special, along with the awkward input layout on most controllers: it is advisable to change the controls to a more congruent assignment; the L or R button, for example.

Attempting to perform the technique in SSB4 and Ultimate results in Lucas's PK Fire weakening the upward ascent of his double jump instead of boosting it, rendering the technique ineffective.

PK Jump & Firebound
is also strangely affected by using PK Fire with his second jump. When the two moves are used simultaneously, he will be propelled forward and slightly higher. This makes for a great approach and extends the special considerably, and can also be used for recovery, acting as a barrier against opponents edgeguarding from below. This works in SSB4 and Ultimate as well.

A variation of this maneuver, known as the Firebound, combines the mechanics of the PK Jump and B-sticking. By pressing the B-stick backwards while holding forward and double jumping, the player will shoot backward; a defensive maneuver. This works in SSB4 as well.

Lucas jump technique
This technique can be executed by playing as Lucas on any stage, and have Lucas grab any item. Then Lucas should jump, and throw the item that he holds upward at the same time as he double jumps. Note that the item used does not have to be a throwing item; battering and shooting items can also be used as well. As with Lucas's PK Fire Zap Jump, attempting to perform this technique in SSB4 and Ultimate results in the upward ascent of Lucas's double jump being weakened altogether instead of getting boosted, rendering the technique ineffective.

Z-air Zap Jump
Similar to Lucas's PK Fire Zap Jump and upward item throw Zap Jump, except that Lucas has to use his grab aerial and double jump at the same time instead of using a PK Fire or throwing an item upward. As with Lucas's PK Fire Zap Jump and upward item throw Zap Jump, attempting to perform this technique in SSB4 and Ultimate results in the upward ascent of Lucas's double jump being weakened altogether instead of getting boosted, rendering the technique ineffective.

Another method can be found here.

PSI Floating
A much easier method of increasing Ness's midair jump height exists exclusively in SSB4, and involves air dodging as Ness uses his midair jump. Dubbed "PSI Floating," this will increase the jump's height by around 25%. This is exclusive to Ness, as attempting to perform it with Lucas or Mewtwo will actually lower their jump height. While this is no longer possible in Ultimate, Ness can still get a similar effect using an aerial, as he could in previous games, and is still the only one of the 3 to be able to do so.