How to order multiple database queries?

I've got a spreadsheet that has 28 different database queries via ODBC connection to a DB2 database.  Most all use the same value to limit the query results and can run in any order.  However, there are a few that are based on the results of one of the others (such as query 10 returns a key that needs to be used in query 20). 

When I do a "Refresh All" what order the queries run in I have no idea.  I know I can control what queries run when I do a "Refresh All" via the property of the query, but it's this dependency that I can't control. 

What I would like to have is let's say a group of 20 queries that run via "Refresh All" (actually I have it where they kick off when a formula value changes) and then a few that run when a dependent query completes.  Any guidance would be appreciated.