Nuclear Option
In NASA's 2007 report to Congress, stand off nuclear detonation can be 10-100 times more effective than kinetic impactor approach. Also, the report indicates that surface or sub-surface detonation is 10-100 times more effective than stand off detonation, although they may present more developmental and operational challenges. The report also mentions use of a nuclear device would likely require prior international coordination, due to the restrictions found in the Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies.
For asteroid over 1 km, the nuclear option practically is the only option at our present technology. A 10 km asteroid require not 10 times, but 1,000 times more effective measure, because the weight is the product of density and volume, and volume is cube of the length.
Despite the political challenges of development of nuclear weapons, because of the effectiveness, they need to be developed and tested for validation.