In Rubinstein and Scharlemann [Geom. Topol. Monogr. 2 (1999) 489-553], the given
list of ways in which a closed orientable 3–manifold could have distinct genus two
Heegaard splittings misses a significant case. A brief description of the case
(discovered by John Berge) is given here, and the proof that the list is complete is
corrected, now incorporating the missed case. Full details and further discussion
appear elsewhere.