Field line reconnection in the wake of coronal mass ejections (CMEs) is a fundamental aspect of some magnetically driven eruptive flare/CME models, e.g., the standard reconnection model Svestka and Cliver, 1992>. This model features a growing hot loop arcade beneath a rising X-type neutral point that is connected to the retreating CME. In models invoking reconnection the rising CME and neutral point are connected by a stretched current sheet. Two recent models, Lin and Forbes <2000> and Linker et al. <2003>, predict that an extended, long-lived current sheet must be formed for any physically plausible reconnection rate. Lin and Forbes derive estimates for heights or lengths of current sheets and the energy input as functions of time. In a previous observational study of SMM CMEs observed from 1984--1989 having candidate magnetic disconnection features, primarily transient concave-outward bright regions following the CME leading edge, we found that about half were followed by coaxial, bright rays suggestive of newly formed current sheets. The rays appeared relatively suddenly several hours after the main CME had left the field of view. In this paper we present the results of analysis of these structures, including their heights and lengths, widths, alignments, and motions, all as functions of time, and show that they are consistent with the existence of current sheets lasting for several hours and extending more than five solar radii into the outer corona.