tracking two git branches at once

[Graham Percival]

Is there a way to keep two branches on my filesystem at once?  Err, this 
is probably a bad way of phrasing the question, so I'll just describe 
the problem:

Most of the time I track master.  I have the documentation built, so 
whenever I make a change it only takes a few minutes to compile the 
changed the files.

Occasionally I want to make a one-line change to web/master.  If I just 
do "git checkout web/master", then I get a weird mixture of master and 
web/master (because git doesn't remove my Documentation/ because I have 
compiled files in there).  I can avoid this weird mixture by deleting 
all the files before checking out the new branch, but then when I go 
back to master, it takes me an hour to compile all the docs.  As a 
result, I tend to wait for a week or two before making changes to 
web/master.

Can I have a pair of directories like
lily-main/master
lily-main/web

which track different branches of git?  (ie without downloading all 
changes twice)

Cheers,
- Graham