Thanks once more:
    index-file.names = ( "BackupPC_Admin.cgi" )
does the job - using http://<site>/backuppc now works as it should, no 
need any more to append the name of the cgi file.

However,
     cgi.assign += ( ".cgi" => "" )
does mischief - it makes lighttpd forget that it must call the cgi code 
when it sees a <filename>.cgi> file - my script only works if I keep
     cgi.assign = ( ".cgi" => "/usr/bin/perl" )
which looks normal to me.

I append the significant part of my script. Principal difference with 
respect to the template script from the sourceforge howto:
   - authentification is skipped for local calls on the server
   - the URL can be <site>/backuppc/?host=<client-name> - something you
     frequently want and which suppresses the need to start with the
     server page (in my mozilla taskbar I have a folder with backuppc
     URLs which behaves like a pulldown menu - server, pc1, pc2 ...)

---------

$HTTP["host"] =~ "^pcjuergen($|.unige.ch)" {
     $HTTP["url"] =~ "^/backuppc($|/)" {
        server.document-root = "/var/www/backuppc"
        alias.url = ( "/backuppc" => "/var/www/backuppc" )
        dir-listing.activate = "disable"
        index-file.names = ( "BackupPC_Admin.cgi" )
        $HTTP["remoteip"] != "127.0.0.1" {
            auth.backend = "htpasswd"
            auth.backend.htpasswd.userfile = "/var/www/passwd/lighttpd"
            auth.require += ( "" => (   "method" => "basic",
                                        "realm" => "BackupPC",
                                        "require" => "valid-user" ) )
        }
     }
     $HTTP["url"] =~ "^/webdav($|/)" {
        $HTTP["url"] =~ "^/webdav/fox_" {

              etc.

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