In this paper we present a new characterization of switch-regular upward embeddings, a concept introduced by Di Battista and Liotta in 1998. This characterization allows us to define a new efficient algorithm for computing upward planar drawings of embedded planar digraphs. If compared with a popular approach described by Bertolazzi, Di Battista, Liotta, and Mannino, our algorithm computes drawings that are significantly better in terms of total edge length and aspect ratio, especially for low-density digraphs. Also, we experimentally prove that the running time of the drawing process is reduced in most cases. Article Type Communicated by Submitted Revised regular paper M. Kaufmann March 2005 March 2006 This work is partially supported by the MIUR Project ALGO-NEXT: Algorithms for the Next Generation Internet and Web: Methodologies, Design and Applications