A three-dimensional model is presented for the hydraulic conductivity and diffusive permeability of capillary endothelial clefts with a junctional strand with discrete pores and a fiber matrix in its wide parts. The model attempts to provide new insight into long-standing issues concerning the relative importance of open junction discontinuities, restricted slit regions, and matrix components in determining the permeability and selectivity of the capillary wall. The predictions drawn from the model are used to formulate new experiments to test two hypotheses concerning the molecular organization of the junction strand and the location of matrix structures in the wide part of the cleft. Using the three-dimensional theoretical approach recently developed by Tsay, Weinbaum, and Pfeffer (Chem. Eng. Comm. 82, 67-102, 1989), the model first explores the behavior of three different molecular models for the junctional strand discontinuities: (i) a more frequent circular pore of 5.5-nm radius formed by isolated missing junction proteins; (ii) a restricted rectangular slit of four to eight missing proteins and 8-nm gap height; and (iii) larger more infrequent breaks of four to eight missing proteins with a gap height of 22 nm, equal to the width of the wide part of the cleft. For the circular and 8-nm gap height pores the primary molecular sieve can be located at the level of the junction strand, whereas for the 22-nm gap height pores, matrix components must be present in at least some portion of the cleft to provide the molecular filter. The water flow through the cross-bridging fibers in the wide part of the cleft is described either by a new exact three-dimensional theory (Tsay and Weinbaum, J. Fluid Mech. 226, 125-148, 1991) for an ordered periodic array or by a new approximate theory for a random array of perpendicular fibers. Both this theory and the new approximate theory for diffusion presented herein take into account for the first time the interaction between the fibers and plasmalemma boundaries. The principal predictions of the model are that (i) infrequent larger breaks are most likely required to account for small solute permeability; (ii) these larger breaks must be accompanied by a sieving matrix, but this matrix probably occupies only a small portion of the depth of the cleft and/or its entrance at the luminal surface; (iii) neither junctional pore, restricted slit, or fiber matrix models can by themselves satisfy permeability and selectivity data; and (iv) one-dimensional models are a poor description of a cleft with infrequent larger breaks since the solute will be confined to small wakelike regions on the downstream side of the junction strand discontinuities and thus not fill the wide part of the cleft.