Eight structurally preserved specimens originally called Cladoxylon onteorense nom. nud. Hueber 1959, from Hensonville, New York, Cladoxylon dichotomum nom. nud. Hueber 1960 from East Ashland, N.Y., and Cladoxylon hueberi Matten 1974 from East Ashland and Cairo, N.Y., are analyzed in detail for their morphological and systematic significance. The type of C. hueberi from East Ashland, by far the most important specimen, provides the first opportunity in any Devonian member of the Cladoxylopsida for a realistic three-dimensional assessment of the primary xylem system. A main axis contains a highly dissected primary xylem system with 40–50 longitudinally anastomosing primary xylem segments. Distally, the main axis dichotomizes producing two equal branches with 20–25 xylem segments each. The outermost primary xylem consists of a system of radially oriented tracheid plates variously interconnected toward the inside, each with a conspicuous protoxylem strand near the xylem periphery. Traces to densely and three-dimensionally, but not helically, arranged lateral appendages depart singly or in groups of two or three from one to three adjacent peripheral-radial xylem plates. Although direct evidence on the external morphology of lateral appendages is not preserved, many trace groups exhibit conspicuous bilateral symmetry consistent with the interpretation of planate lateral appendages similar to those described for Pseudosporochnus nodosus. Other trace groups may indicate more three-dimensional lateral appendages. One sub-opposite pair of clepsydroid traces is borne at right angles to, and in obvious relationship with, the dichotomy of the main axis. Cortex is heterogeneous, consisting of thin-walled parenchyma with embedded clusters of sclereids and thick-walled parenchyma. These clusters appear responsible for a regular pattern of bumps or pits in compressed regions of the specimen and are closely comparable to those observed in Pseudosporochnus nodosus. A systematic analysis, attempting to view fragmentary evidence from both compressions and permineralizations in a single coherent framework, leads us to hypothesize assignment of the East Ashland and Hensoville specimens to the genus Pseudosporochnus. Although supported by the evidence, the hypothesis of assignment is by no means proven. We propose it, however, because we think that advancing systematic hypotheses conspicuously at risk of being refuted by additional observation promotes far greater understanding than taking an agnostic stance toward systematics implied by the use of “form” taxa. We further clarify our position by suggesting specific observations likely to be made from fossil specimens that might refute our hypothesis.