Today I have a specimen of what I believe is Composita subtilita from the Carboniferous (Mississippian epoch, Visean stage of the ICS or Mississippian period, Chesterian stage in the US) rocks of Utah. It was found near Conger Springs which is about 63 miles (as the crow flies) west of the town of Delta in Millard County. The rocks exposed at Conger springs are the Chainman formation and are the youngest Mississippian layers before changing to the Pennsylvanian. The shell of Composita subtilita is round to ovate with a fold in the pedicle valve that corresponds to a sulcus in the brachial valve. The fold is shallow at the beak and gets gradually wider and deeper as it progresses to the anterior margins. Both valves are equally convex and are widest about mid way between the anterior and posterior.
I used the reference "Brachiopoda of the Amsden Formation (Mississippian and Pennsylvanian) of Wyoming.", MacKenzie Gordon, Jr., 1975 pg. 64, plate 10, fig 33-37 to identify this brachiopod.