A new process concept is outlined to utilize low and high pressure feed streams efficiently in a single pressure swing adsorption (PSA) process. The low pressure feed is processed first in the PSA unit to produce low pressure product. Following this, the high pressure stream is processed in the same unit. Low pressure generated in the first part of the process is used internally in the process to assist the production of high pressure product. Essentially 100% recovery of the high pressure product is possible. This is achieved in a single unit without the need to store gas product during the intermediate process steps. The process concept is demonstrated for pure hydrogen production. A process is simulated in which two streams, both containing 25% methane and 75% hydrogen at two different pressures, are supplied to a single PSA unit. The simulation shows that, using a five-bed process, one can produce 100% high pressure hydrogen at ultra-high purities (i.e. ppm levels of methane in the product). If the low pressure stream is not integrated, then the maximum high pressure H-2 recovery is only 85%.