A finger cover, such as a finger wipe that can fit onto a human finger, is provided with an improved seam structure. The cover includes a pocket member having an open end for the insertion of a finger. The pocket member is formed by a first panel attached to a second panel along a flush outwardly facing circumferential edge seam. The seam is less than about 1 millimeter (mm) in width and about 1 mm in height. Additional reinforcing weld points may be provided at various locations along the seam.