Measurements of suprathermal electron fluxes in the solar wind indicate that field lines within coronal mass ejections, CMEs, near and beyond 1 AU are normally connected to the Sun at both ends. However, on occasion some field lines embedded deep within CMEs appear to be connected to the Sun at only one end. Here we propose an explanation for how such field lines arise in terms of 3-dimensional reconnection close to the Sun. Such reconnection also provides a natural explanation for the flux rope topology characteristic of many CMEs as well as the coronal loops formed during long-duration, solar soft X-ray events. Our consideration of the field topologies resulting from 3-dimensional reconnection indicates that field lines within and near CMEs may on occasion be connected to the outer heliosphere at both ends. ¿ American Geophysical Union 1995