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 air jump propels him by 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.

PK Jump & Firebound

Ness 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 Smash 4 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 also works in Smash 4 as well.

Lucas jump technique

This technique can be executed by playing as Lucas at any stage, and have Lucas grab any item. Then Lucas should jump, and throw the item that he holds upwards at the same time as he double jumps. Note that the item used doesn't have to be a throwing item, a batting item can also be used as long the item can be thrown away. This also works with Ray Gun and Super Scope, while shooting them.

Z-air Zap Jump

Similar to Lucas' Zap Jump and item throw Zap Jump except Lucas has to use his Z-air and double jump at the same time instead of using a PK Fire or throwing an item.

Another method can be found here.

PSI Floating

A much easier method of increasing Ness' midair jump height exists in SSB4 and involves airdodging as he 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.