Waterman Method

The Waterman Method is a method for solving the 3x3x3 Cube which was invented by Marc Waterman in the 1980s. The method is based on Corners First methods but is efficient enough to be used for advanced speedsolving (average times of under 20 seconds).
History
The method was developed by Marc Waterman and his friend Daan Krammer in 1981. Marc added "a lot of additional processes and shortcuts" to achieve a sub17second average by the mid1980s (Minh Thai's 1982 "world record" by comparison was 22.95 seconds). The method seems to have been littleknown however. When cubing revived in the late 1990s Jessica Fridrich put her algorithms on her webpage leading to the rise of CFOP as a main speedcubing method. Although many websites mentioned the Waterman Method, its details were nowhere to be found.[1] In August 2004 Josef Jelínek contacted Marc Waterman[2] and obtained information about the method which he placed on his rubikscube.info website.
Classification
It has occasionally been questioned as to whether the Waterman method is a true Corners First method. According to Josef Jelínek:[3]
Waterman's method can be considered pure Cornersfirst. The main reason for that is that you can solve all corners first before starting solving edges without any change to the sequences used or a method itself except for swapping two steps. The reason Marc solved one layer completely first was probably because he was used to do it like that. It is sometimes (often) easy to see how to put some edges (and a center) to the first layer during completing the first four corners, so reducing the number of turns required for the first layer. CLL sequences used preserve the first layer. Personally, I solve all corners first + some obvious edges of the first layer.
Steps
The steps are as follows:
 Solve one layer of the cube. The original way to do this is by first putting together the corners and then solving the center and edges together. This can also be done with block building (start with a 1x2x3 block as with Roux and then fill in the last three pieces).
 Solve the corners of the opposite layer. This is done in one step in the style of CxLL. After this step, turn the cube so that the solved layer is on L.
 Solve two of the edges on R, while at the same time placing a third somewhere in the R layer. Finish the R edges while orienting the M edges, all in one algorithm. This step is difficult to learn and has around 80 algorithms, but the algorithms mostly use only M, R, r, and U moves, so this is a fast step. Step 3c: Solve the M edges. This is trivial and there are only a few possible cases, all very fast.
If you are interested in learning this method you should check out Josef Jelinek's webpage which has very thorough descriptions as well as a complete list of algorithms for the last four steps. He also has a copy of the original booklet containing the method.