Changing Pulldown selection causes upstream search to run again

I'm building a view that roughly looks like this:

TimeRangePicker
  Search using inputlookup
    Pulldown populated by Search above
      Search building larger result set
        Pulldown using static config
          Pulldown using static config
            PostProcess applying selections from previous two Pulldowns as filter for larger result set
              Pager
                Table
                  ...more stuff...

Ideally, I'd want the Search 2 result set to be filtered whenever the Pulldown 2 or 3 is changed - without re-running Search 2. I'd expect this to work because Search 2 is upstream from Pulldown 2 and 3.

However, when I change the selection on Pulldown 2 or 3 the upstream Search 2 is run again. Any ideas?