The New Tetris, Square mode of Tetris Worlds, and Lockjaw: The Overdose reward the player for creating 4x4 block squares out of four tetrominoes. Building wide platforms (flat top sides) into the top of a square in progress allows more than one such square to be built at once, keeping options open for handling any tetromino.

The New Tetris was developed prior to the standardization of tetromino colors. The diagrams below, like most other diagrams in Hard Drop, use Tetris Worlds colors per the more recent Tetris Guideline.

Monosquares

Spiral J monosquare

It is best to build J and L monosquares using this spiral method so that platform width is maximised as early as possible.

L on the left and J on the right require a double slide. L on the right and J on the left require a double slide if there isn't enough support below. See below.

Spiral L monosquare

Non-spiral L and J monosquares

One side of each of the spiral monosquares depicted above requires a double slide. These squares are built on the same side and do not require a double slide if built on top of a 3-block platform.

T monosquare

Building a T monosquare quickly

If three T pieces are readily available and there is only a platform one block wide upon which to build, it is wise to build in a slightly different way:

O monosquare

I monosquare

2×4 constructions

If two of the same 2×4 constructions are put together, monosquares are formed. Alternatively, two different 2×4s can be put together (or one sandwiched between two I pieces) to make multisquares in addition to those below.

Multisquares

Most of these multisquares can be constructed in different rotations, with the pieces being added in different orders or with an I piece on the opposite side. The following are some of the most efficient ways of building them.

SJSJ and ZLZL

JSSJ and LZZL

ZLLZ and SJJS

This is possible in The New Tetris but relies on uncommon wall kicks: see Tactical rotation#S/Z pop. SJJS is also possible in TOD rotation by rotating S twice and then rotating left once it's on the J.

ZLTT and SJTT

STTJ and ZTTL

TZTJ and TSTL

TTLZ and TTJS

This requires the same move as for the ZLLZ and SJJS multisquares, and is good to fall back on in the middle of building a T monosquare.

LTZT and JTST

LTTI and JTTI

TTLI and TTJI

Similarly to TTLZ and TTJS, good to fall back on when a T monosquare is abandoned.

ZLJI and SJLI

JSLI and LZJI

LJZI and JLSI

This requires the same move as the ZLLZ and SJJS multisquares. It is of course best built with the I on the other side if the I, J/L and Z/S are available already

LSIL and JZIJ

Requiring double slide (or tactical rotation)

With I before S or Z (triple slide or tactical rotation in addition to the moves above):

IJLO and ILJO

As with many of these multisquares, the I can be on the other side and added last if the other pieces are all available already.

JJOI and LLOI

Good to fall back on midway into a spiral L or J monosquare.

Double slide

In some cases a piece must be moved sideways two or more spaces before dropping at all. The New Tetris's smooth tetromino falling animation often means this can't be done – pieces can't be moved to sit on a ledge too far under an overhang. There are methods to get around this: tactical rotation.