An end effector for a surgical stapler, said end effector comprising: a staple cartridge, said staple cartridge comprising: a cartridge body comprising a support portion, wherein said support portion comprises a plurality of staple cavities, and wherein each said staple cavity comprises an opening; and a plurality of staples, wherein at least a portion of each said staple is removably stored within a said staple cavity, wherein each said staple is movable between an unfired position and a fired position, wherein each said staple is deformable between an unfired configuration and a fired configuration when each said staple is moved between said unfired position and said fired position; an anvil comprising a plurality of staple pockets each adapted to deform a respective staple from its unfired configuration to its fired configuration as it is moved from its unfired position to its fired position; and a compressible tissue thickness compensator (10020, 10320, 10420, 10520, 10620, 10720, 10820, 10920, 11320, 11520, 13020, 16620) configured to be captured within said staples, wherein said compressed tissue thickness compensator may assume different compressed heights within different said staples, wherein said anvil is movable relative to said staple cartridge from an open position in which tissue to be stapled is received and a closed position in which said tissue is compressed between said anvil and said compressible tissue thickness compensator, wherein said support portion and said anvil define a fixed tissue gap in the closed position such that said staples may be deformed to a predetermined height, characterized in that said tissue thickness compensator has an uncompressed height that is greater than the predetermined deformed height of said staples. a staple cartridge, said staple cartridge comprising: a cartridge body comprising a support portion, wherein said support portion comprises a plurality of staple cavities, and wherein each said staple cavity comprises an opening; and a plurality of staples, wherein at least a portion of each said staple is removably stored within a said staple cavity, wherein each said staple is movable between an unfired position and a fired position, wherein each said staple is deformable between an unfired configuration and a fired configuration when each said staple is moved between said unfired position and said fired position; a cartridge body comprising a support portion, wherein said support portion comprises a plurality of staple cavities, and wherein each said staple cavity comprises an opening; and a plurality of staples, wherein at least a portion of each said staple is removably stored within a said staple cavity, wherein each said staple is movable between an unfired position and a fired position, wherein each said staple is deformable between an unfired configuration and a fired configuration when each said staple is moved between said unfired position and said fired position; an anvil comprising a plurality of staple pockets each adapted to deform a respective staple from its unfired configuration to its fired configuration as it is moved from its unfired position to its fired position; and a compressible tissue thickness compensator (10020, 10320, 10420, 10520, 10620, 10720, 10820, 10920, 11320, 11520, 13020, 16620) configured to be captured within said staples, wherein said compressed tissue thickness compensator may assume different compressed heights within different said staples,