This paper is a refinement of the author’s previous work [ibid. 82, 407- 410 (1981; Zbl 0477.32030)]. Let M be an algebraic compactification of a strongly pseudoconvex non-Stein surface. The author uses Kodaira’s classification of algebraic surfaces, eliminates certain possibilities for M by studying the actions of holomorphic automorphisms, and gives explicit examples to show that each of the remaining possibilities can occur. The kinds that actually occur are: (a) rational surfaces, (b) nonrational ruled surfaces, (c) K3 surfaces, (d) Enriques surfaces, (e) elliptic surfaces, (f) surfaces of general type. The author also proves that every compactifiable strongly pseudoconvex surface is quasi- projective.