Marc Waterman and Daan Krammar developed the Waterman method for solving the cube in 1982. It has never been a particularly popular method, but it's an interesting case of a relatively fast and decent corners-first method.
The only website which currently appears to have a full description of the method is rubikscube.info by Josef Jelinek, buuut that website has not been updated in about 15 years, and the description is incomplete. It does have a PDF version of the original booklet describing the method, but it's not accessible, and hard to read. So I thought I'd describe the method in full here, with all the algorithms.
There are four main steps in the Waterman method:
Occasionally you may see an (R) in these algorithms. This doesn't mean what it normally means in algorithms, this is not a finger trick. For more information, look here.