A surgical instrument, comprising: a jaw member, comprising: an elongate slot extending along a longitudinal axis; a first outer surface on a first side of said elongate slot; and a second outer surface on a second side of said elongate slot opposite said first side; and a compressible adjunct assembly, comprising: an attachment layer, comprising: a first section, on said first side of said elongate slot, wherein said first section is attached to said first outer surface; a second section, on said second side of said elongate slot, wherein said second section is attached to said second outer surface; and an intermediary section extending between said first section and said second section, wherein said intermediary section at least partially bridges said elongate slot; a first compressible adjunct on said first side of said elongate slot; and a second compressible adjunct on said second side of said elongate slot, wherein said first compressible adjunct is spaced apart from said second compressible adjunct, wherein said first section is attached to said first compressible adjunct, and wherein said second section is attached to said second compressible adjunct, characterized in that said intermediary section comprises a bar extending along a length of said intermediary section, wherein said bar is stepped up from said first section, and wherein said bar is stepped up from said second section, and wherein said bar protrudes into a gap defined between said first compressible adjunct and said second compressible adjunct. a jaw member, comprising: an elongate slot extending along a longitudinal axis; a first outer surface on a first side of said elongate slot; and a second outer surface on a second side of said elongate slot opposite said first side; and an elongate slot extending along a longitudinal axis; a first outer surface on a first side of said elongate slot; and a second outer surface on a second side of said elongate slot opposite said first side; and a compressible adjunct assembly, comprising: an attachment layer, comprising: a first section, on said first side of said elongate slot, wherein said first section is attached to said first outer surface; a second section, on said second side of said elongate slot, wherein said second section is attached to said second outer surface; and an intermediary section extending between said first section and said second section, wherein said intermediary section at least partially bridges said elongate slot; a first compressible adjunct on said first side of said elongate slot; and a second compressible adjunct on said second side of said elongate slot, wherein said first compressible adjunct is spaced apart from said second compressible adjunct, wherein said first section is attached to said first compressible adjunct, and wherein said second section is attached to said second compressible adjunct, characterized in that said intermediary section comprises a bar extending along a length of said intermediary section, wherein said bar is stepped up from said first section, and wherein said bar is stepped up from said second section, and wherein said bar protrudes into a gap defined between said first compressible adjunct and said second compressible adjunct. an attachment layer, comprising: a first section, on said first side of said elongate slot, wherein said first section is attached to said first outer surface; a second section, on said second side of said elongate slot, wherein said second section is attached to said second outer surface; and an intermediary section extending between said first section and said second section, wherein said intermediary section at least partially bridges said elongate slot; a first compressible adjunct on said first side of said elongate slot; and a second compressible adjunct on said second side of said elongate slot, wherein said first compressible adjunct is spaced apart from said second compressible adjunct, wherein said first section is attached to said first compressible adjunct, and wherein said second section is attached to said second compressible adjunct, characterized in that said intermediary section comprises a bar extending along a length of said intermediary section, wherein said bar is stepped up from said first section, and wherein said bar is stepped up from said second section, and wherein said bar protrudes into a gap defined between said first compressible adjunct and said second compressible adjunct.