The present invention provides a method and apparatus for extracting liquid water from moist air using minimal energy input. The method can be considered as four phases: (1) adsorbing water from air into a desiccant, (2) isolating the water-laden desiccant from the air source, (3) desorbing water as vapor from the desiccant into a chamber, and (4) isolating the desiccant from the chamber, and compressing the vapor in the chamber to form liquid condensate. The liquid condensate can be removed for use. Careful design of the dead volumes and pressure balances can minimize the energy required. The dried air can be exchanged for fresh moist air and the process repeated. An apparatus comprises a first chamber in fluid communication with a desiccant, and having ports to intake moist air and exhaust dried air. The apparatus also comprises a second chamber in fluid communication with the desiccant. The second chamber allows variable internal pressure, and has a port for removal of liquid condensate. Each chamber can be configured to be isolated or in communication with the desiccant. The first chamber can be configured to be isolated or in communication with a course of moist air. Various arrangements of valves, pistons, and chambers are described.