A geometric analysis of fenestrate bryozoan lophophore shape and arrangement is conducted by creating a theoretical morphospace of apertural positioning within the colonial meshwork. Working from the assumption that fenestrate bryozoans needed to form a continuous filtering surface with contact between adjacent lophophores, we show that within the morphospace three regions exist for optimum close-packing of lophophores with circular projections; all other close-packing configurations in the morphospace require the existence of noncircular lophophores.Examination of the actual distribution of 251 fenestrate colonies within the morphospace reveals that the morphospace regions occupied by fenestellids and polyporids are displaced and have little overlap, but that they are very similar in size and shape, and that the colonies scale similarly. With increasing size, fenestrate meshworks expand laterally faster than the branches widen and the proximodistal spacing of the apertures increases, apparently because the larger zooids require disproportionately more room for their lophophores.Two of the optimum close-packing regions of the morphospace are occupied by fenestrates. The positioning of the fenestellid region within the morphospace suggests that these biserial bryozoans followed a proximodistal-row placement of the lophophores, and that the lophophores were generally equitentacular, with circular projections. The positioning of the polyporid region within the morphospace suggests that these polyserial bryozoans followed a diagonal-row placement of the lophophores, and that the lophophores were heteromorphic, with medial lophophores on the branch being more equitentacular whereas the laterally placed lophophores were obliquely truncate. The third optimum close-packing region in the morphospace, corresponding to a hypothetical lateral-row placement of the lophophores within the colony, is unoccupied. We suggest that hypothetical fenestrate morphologies in the vacant region of morphospace have branches that would be too narrow to support normally shaped zooids, and that the lateral-row placement of the lophophores would have required the branches of the colony to have been perfectly aligned throughout growth.