The integral equation analysis of large perfect electric conductor bodies is commonly formulated in terms of combined field integral equations (CFIE) that avoid spurious internal resonances. The dual-surface electric field integral equation (DSEFIE) is a less employed alternative approach; we discuss here how to cure its shortcomings and enhance its advantages over the CFIE for large bodies of nontrivial geometrical complexity. We study the convergence and accuracy of the DSEFIE also with respect to the current state of the art in the testing of the magnetic field integral equation. Examples of applications to large and realistic composite structures show the effectiveness of the proposed approach.