Strategic Command does missile Defense???

We've all heard about the National Missile Defense System that is being developed. The goal is to provide a system to protect the USA from ballistic missiles.

I was under the impression that since Missile defense is an extention of Air Defense, that the National Missile Defense system would be controlled by NORAD, which as we know is tasked with air and space defense for North America. However, I just found this:

The Joint Functional Component Command for Integrated Missile Defense (JFCC-IMD) was established to optimize planning, execution and force management, as directed by HQ USSTRATCOM, of deterring attacks against the United States, its territories, possessions and bases. In addition, JFCC-IMD would employ appropriate forces, should deterrence fail, and the associated mission of planning, integrating and coordinating global missile defense operations and support for missile defense.

Strategic Command- Integrated Missile Defense

If NORAD controls air and space defense, Why is US Strategic Command in charge of the national missile defense system? Shouldn't that fall under NORAD?

Tim