If you put your <Context> fragment in
conf/[enginename]/[hostname]/dir1#dir2#appname.xml
you can access the webapp via
http://[hostname]/dir1/dir2/appname, which
I think is what you want. Haven't been able to find this in the Tomcat
doc yet, but I did test it successfully on 5.5.9. Have no idea if this
trick with the # would work on the name of a .war file.