Because he had designed the Discovery, Curnow was one of three Americans, along with Dr. Chandra and Heywood Floyd, chosen to participate in a second mission towards Jupiter, this time aboard the Russian spaceship Cosmonaut Alexei Leonov. During the initial trip, Curnow was placed into Suspended Animation, but was revived when the ship arrived.
When the Discovery was found, Curnow, along with Soviet astronaut Maxim Brajlovsky, were selected for the task of re-entering the ship. The two managed to enter through the emergency airlock, and discovered that the ship still had a breathable atmosphere. After exploring the ship, they manged to restart it's main functions.
When a Monolith was discovered in orbit around Jupiter, Curnow monitored Max as he examined it in an extravehicular pod. He was also the first to notice a problem, but was unable to get Max away before his pod was destroyed.
After the mission was over, and the Leonov left Jupiter's orbit, Curnow was once again placed into suspended animation. In the novel, it is mentioned that he marries Katerina Rudenko. He also died at some point prior to 2061.