I'm trying to sort out network analysis in ArcGIS 10.
Toy example of finding shortest distance between two points looks something like that :

Where squares are two locations, and the green line is an output from Closest Facility tool.
What I need to do, is to restrict motorways and slip roads from the analysis. So the new route should avouid the red segments:

What is the best strategy to proceed in such case?
Should I edit my network and delete all the segments I do not want to have in analysis? Or perhaps use linear Barriers?
Thanks for help!