Lighttpd

We have an nginx proxy at tools.wmflabs.org that receives requests by http and https and passes them by http on to lighttpds on a grid (one lighttpd per top-level path). Requests that reach the proxy by https are received by the lighttpds like this:

HEAD /lighttpd-test/test HTTP/1.1
Connection: close
Host: tools.wmflabs.org
X-Forwarded-Proto: https
X-Original-URI: /lighttpd-test/test
User-Agent: curl/7.29.0
Accept: */*

This works great except in the case where the URL references a physical directory and misses the trailing slash ("/"), as lighttpd then generates a redirect to the http URL:

HTTP/1.1 301 Moved Permanently
Location: http://tools.wmflabs.org/lighttpd-test/test/
Connection: close
Date: Fri, 06 Jun 2014 14:50:29 GMT
Server: lighttpd/1.4.28

The relevant parts of our lighttpd configurations are:

server.modules = (
  "mod_setenv",
  "mod_access",
  "mod_accesslog",
  "mod_alias",
  "mod_compress",
  "mod_redirect",
  "mod_rewrite",
  "mod_fastcgi",
  "mod_cgi",
)

server.port = $port
[...]
server.document-root = "$home/public_html" 
[...]
server.follow-symlink = "enable" 
[...]
server.stat-cache-engine = "fam" 
ssl.engine = "disable" 

alias.url = ( "/$tool" => "$home/public_html/" )

index-file.names = ( "index.php", "index.html", "index.htm" )
dir-listing.encoding = "utf-8" 
server.dir-listing = "disable" 
url.access-deny = ( "~", ".inc" )
[...]

How can I make lighttpd respect X-Forwarded-Proto and use it when constructing redirects for directories? I'm aware that I could try to tackle this in nginx, but I'd prefer if I can fix it in lighttpd.