Abstract: A method of compressing a compressible fluid, using a hydraulically driven compressor comprising a precompressor, a first cylinder, and a second cylinder. The precompressor receives a low pressure input of compressible fluid and fills the first cylinder to a precompressor output target pressure. A piston within the first cylinder then forces the compressible fluid into the second cylinder. This cycle is repeated until the second cylinder is filled to a first-cylinder output target pressure, whereupon a piston within the second cylinder forces the compressible fluid out of the second cylinder as a high pressure compressible fluid output, typically into some sort of storage vessel. This cycle is repeated until the compressible fluid output pressure reaches a second-cylinder output target pressure.