Compressible reclosable storage containers (e.g., pouches) having a one-way valve disposed along the bottom of the container. In one configuration, the reclosable pouch comprises a receptacle having a storage chamber and a mouth in communication with the storage chamber, and an airtight closure for closing the mouth. The receptacle comprises two walls made of thermoplastic web material, two side seals that include respective marginal portions of the two walls, and a vent that extends from one side seal to the other. The vent comprises a multiplicity of collapsible channels, each channel comprising a respective air inlet in flow communication with the storage chamber and a respective air outlet in flow communication with space external to the pouch. The channels may be formed by a series of zigzag or wave-shaped heat seals or heat seals have other shapes.