An apparatus comprising: (a) a body; (b) a shaft assembly extending distally from the body, wherein the shaft assembly has a distal end; (c) a stapling head assembly (600, 700,1200,1400) located at the distal end of the shaft assembly, wherein the stapling head assembly comprises: (i) an annular deck member (650, 702) defining an inner diameter and an outer diameter, wherein the deck member comprises: a first deck surface (670, 672, 674; 738), wherein the first deck surface has a curved profile defined by a curve extending from the inner diameter of the deck member to the outer diameter of the deck member, an outer annular array of staple openings (624; 724), and an inner annular array of staple openings (624; 724), (ii) a plurality of staples, and (iii) a driver operable to drive the staples through the staple openings; and (d) an anvil, wherein the anvil is operable to compress tissue against the first deck surface, wherein the deck member further comprises a second deck surface (660, 722), wherein the second deck surface is recessed relative to the first deck surface (674, 738); and wherein the stapling head assembly defines a longitudinal axis and the second deck surface (660, 722) is obliquely oriented relative to the longitudinal axis such that an outermost portion of the second deck surface is positioned distally relative to an innermost portion of the deck surface, such that the second deck surface slopes proximally from the outermost portion toward the innermost portion, wherein the deck member further comprises a plurality of stand-off features protruding from the second deck surface, wherein the first deck surface is located on the stand-off features. (a) a body; (b) a shaft assembly extending distally from the body, wherein the shaft assembly has a distal end; (c) a stapling head assembly (600, 700,1200,1400) located at the distal end of the shaft assembly, wherein the stapling head assembly comprises: (i) an annular deck member (650, 702) defining an inner diameter and an outer diameter, wherein the deck member comprises: a first deck surface (670, 672, 674; 738), wherein the first deck surface has a curved profile defined by a curve extending from the inner diameter of the deck member to the outer diameter of the deck member, an outer annular array of staple openings (624; 724), and an inner annular array of staple openings (624; 724), (ii) a plurality of staples, and (iii) a driver operable to drive the staples through the staple openings; and (i) an annular deck member (650, 702) defining an inner diameter and an outer diameter, wherein the deck member comprises: a first deck surface (670, 672, 674; 738), wherein the first deck surface has a curved profile defined by a curve extending from the inner diameter of the deck member to the outer diameter of the deck member, an outer annular array of staple openings (624; 724), and an inner annular array of staple openings (624; 724), a first deck surface (670, 672, 674; 738), wherein the first deck surface has a curved profile defined by a curve extending from the inner diameter of the deck member to the outer diameter of the deck member, an outer annular array of staple openings (624; 724), and an inner annular array of staple openings (624; 724), (ii) a plurality of staples, and (iii) a driver operable to drive the staples through the staple openings; and (d) an anvil, wherein the anvil is operable to compress tissue against the first deck surface, wherein the deck member further comprises a second deck surface (660, 722), wherein the second deck surface is recessed relative to the first deck surface (674, 738); and wherein the stapling head assembly defines a longitudinal axis and the second deck surface (660, 722) is obliquely oriented relative to the longitudinal axis such that an outermost portion of the second deck surface is positioned distally relative to an innermost portion of the deck surface, such that the second deck surface slopes proximally from the outermost portion toward the innermost portion, wherein the deck member further comprises a plurality of stand-off features protruding from the second deck surface, wherein the first deck surface is located on the stand-off features.