A dispenser for dispensing fluids comprising: a pump mechanism operative for pumping fluid from a chamber out of an outlet thereby creating vacuum conditions below atmospheric in the chamber, at least two collapsible fluid containing reservoirs enclosed but for each having an outlet passageway in communication with a chamber, a primary one-way valve for each reservoir permitting flow of fluid from each reservoir through the passageway to the chamber when certain vacuum conditions exist in the chamber relative to the reservoir, characterized by; each valve having a threshold vacuum defined as a vacuum in the chamber below a pressure in the respective reservoir for that valve, the threshold vacuum for each valve being different than the threshold vacuum of all the other valves, wherein after the threshold vacuum of one of the primary one-way valves is exceeded by operation of the pump mechanism, that primary one-way valve permitting flow of fluid from its reservoir by further operation of the pump mechanism to create vacuum conditions less than the threshold value of that primary one-way valve and the other primary one-way valves until its reservoir is substantially emptied whereafter further operation of the pump mechanism creates a vacuum in the chamber which exceeds the threshold vacuum for another of the primary one-way valves after which such other of the primary one-way valves permitting flow of fluid from its reservoir by operation of the pump mechanism and, each valve assuming either a sealed condition or an openable condition, in the sealed condition, each valve prevents flow of fluid from its respective reservoir through its passageway to the chamber and is biased to remain in the sealed condition against moving to the openable condition unless the valve is subjected on its chamber side to a vacuum below atmospheric greater than the threshold vacuum for the valve whereupon the valve moves from the sealed condition to the openable condition, in the openable condition: (a) each valve is movable between a closed position and an open position, (b) each valve is biased to return to and remain in the closed position and against moving from the closed position toward the open position other than when subjected to a vacuum below atmospheric greater than an opening vacuum of the valve when the valve moves from the closed position toward the open position permitting flow of fluid from its respective reservoir through its passageway to the chamber, (c) in the closed position, each valve prevents flow of fluid from its respective reservoir through its passageway to the chamber, and (d) in the open position, each valve permits flow of fluid from its respective reservoir through its passageway to the chamber, the threshold vacuum of each valve being a greater vacuum below atmosphere than its opening vacuum and the opening vacuum of all other valves. (a) each valve is movable between a closed position and an open position, (b) each valve is biased to return to and remain in the closed position and against moving from the closed position toward the open position other than when subjected to a vacuum below atmospheric greater than an opening vacuum of the valve when the valve moves from the closed position toward the open position permitting flow of fluid from its respective reservoir through its passageway to the chamber, (c) in the closed position, each valve prevents flow of fluid from its respective reservoir through its passageway to the chamber, and (d) in the open position, each valve permits flow of fluid from its respective reservoir through its passageway to the chamber, the threshold vacuum of each valve being a greater vacuum below atmosphere than its opening vacuum and the opening vacuum of all other valves.