Two approaches to reconstructing the actual pore space of petroleum reservoir rocks in computer memory from serial section data are discussed, The key to success in the reconstruction process is the ability to correctly identify all the necks in the reconstructed 3-D pore space. The performance of a neck identification strategy, using only one scanning orientation but incorporating an estimate of the local orientation of the pore space pathway, is quantitatively assessed using model media and is shown to be an inadequate strategy which misses a large fraction of the pore necks and, therefore, cannot yield a realistic reconstruction of the porous medium, We reiterate that a multiorientation scanning scheme is a necessity for correct and complete neck identification, and, therefore, for successful 3-D reconstruction. Preliminary results indicate that the estimated local orientation of the pore space pathway alpha’ tends to systematically overestimate the actual local orientation alpha and hence its inclusion may not provide a better measurement of neck orientations and areas. More research is needed. Whether or not the estimated local orientation is incorporated, the uncertainty in measurement accuracy grows as the average difference between the true neck orientations and the scanning directions from which they are detected becomes larger, This favors the nine-orientation scanning scheme over the three-orientation scanning scheme, Incorporating an estimate of the local orientation of the pore space pathway into the multiorientational scanning schemes results in substantial reductions in the required resolutions and improvements in the efficiencies of the multiorientation schemes for the simple model media studied. It increases the advantage of the nine-orientation scanning scheme relative to the three-orientation scanning scheme, For complex, real porous media it is not possible to determine whether these gains also would be achieved or would be accompanied by offsetting disadvantages without conducting additional studies with more complex model media, A more accurate and reliable method of estimating the local orientation of the pathway is required before such studies are done, Incorporation of the estimate of local orientation considered in this work into the existing multiorientation software for 3-D reconstruction is not recommended.