I recently ran across a new way to minimize the disruption of my projects that are currently underway from "emergency requests/projects" that come in out of left field. I have found it to be quite effective.
GRD Process - Project Management process for handling out of cycle high priority projects with minimal disruption to in-flight project. GRD team is made up of only team members who are absolutely core to the completion of the emergency project (typically Development, QA, Product). Project Manager exists to communicate status to non core team members (to avoid interruption), to extract information needed from non-core team to resolve any open issues and to aide in the removal of any overall dependencies.
I have found this to be most effective when managing Projects related to Website Feature Development. Typically these projects already have short durations, and the impact that emergency projects/requests have can be tremendous. I have found that putting the GRD process into practice has decreased the disruption from "emergency requests/projects" and kept the team moving along on our current sprint cycle with minimal overall impact/distraction. I simply love it!!!