An end effector system for use with a surgical instrument, wherein said end effector system comprises: an anvil of a first stiffness; a staple cartridge channel configured to receive a staple cartridge therein, wherein said staple cartridge channel is of a second stiffness, wherein said channel comprises channel walls (4334, 4335, 4337) each channel wall comprising: a proximal zone in which said channel wall comprises a proximal wall portion having a first width; and a distal zone in which said channel wall comprises a distal wall portion having a second width, wherein said second width is greater than said first width; and wherein said anvil comprises proximal surrounding portions configured to surround said proximal wall portions when said end effector system is in a fully clamped configuration, wherein each proximal surrounding portion comprises a lower portion, an upper portion and a ledge defined therebetween, wherein the lower portion is configured to overlap the respective proximal wall portion when said end effector system is in said fully clamped configuration, wherein the upper portion is thicker than the lower portion, and said proximal wall portions each comprise a ledge, and wherein each ledge of said proximal wall portions faces said respective ledge of said proximal surrounding portion when said end effector system is in said fully clamped configuration, wherein each proximal wall portion comprises a cutout comprising a wall thickness that is less than that of the distal wall portion, such that some of the stiffness of the staple cartridge channel is sacrificed to stiffen the anvil, whilst maintaining a desirable instrument diameter. an anvil of a first stiffness; a staple cartridge channel configured to receive a staple cartridge therein, wherein said staple cartridge channel is of a second stiffness, wherein said channel comprises channel walls (4334, 4335, 4337) each channel wall comprising: a proximal zone in which said channel wall comprises a proximal wall portion having a first width; and a distal zone in which said channel wall comprises a distal wall portion having a second width, wherein said second width is greater than said first width; and a proximal zone in which said channel wall comprises a proximal wall portion having a first width; and a distal zone in which said channel wall comprises a distal wall portion having a second width, wherein said second width is greater than said first width; and wherein said anvil comprises proximal surrounding portions configured to surround said proximal wall portions when said end effector system is in a fully clamped configuration, wherein each proximal surrounding portion comprises a lower portion, an upper portion and a ledge defined therebetween, wherein the lower portion is configured to overlap the respective proximal wall portion when said end effector system is in said fully clamped configuration, wherein the upper portion is thicker than the lower portion, and said proximal wall portions each comprise a ledge, and wherein each ledge of said proximal wall portions faces said respective ledge of said proximal surrounding portion when said end effector system is in said fully clamped configuration, wherein each proximal wall portion comprises a cutout comprising a wall thickness that is less than that of the distal wall portion, such that some of the stiffness of the staple cartridge channel is sacrificed to stiffen the anvil, whilst maintaining a desirable instrument diameter.