Past U.S.-North Korea negotiations on nuclear issues can be roughly classified into two types.
The first type relates to the Framework Agreement of the Clinton administration. The basic assessment from documents of the period was that a military confrontation might result in nearly 1 million military and civilian casualties, so the only option was compromise. The main points of compromise were that North Korea would freeze operations at the Yongbyon nuclear facility under the inspections of the International Atomic Energy Agency and, in return, would receive supplies of heavy fuel oil and construction of a light-water nuclear reactor for power generation. North Korea abided by this compromise from 1994 to 2002.
The second type of negotiations relates to former U.S. President George W. Bush's policy of calling North Korea part of the "axis of evil." This policy was implicitly based on the assumption that North Korea would collapse.