Run native binary CGI on lighttpd

Question

Hello, I'm trying to set up lighttpd to run binary CGI app (not PHP script or smth, but a binary file, compiled from C++ source). I actually have

server.modules = (
...
"mod_cgi"
...
)

uncommented, have myApp.exe in htdocs/app, and also

cgi.assign = ( "myApp.exe" => "myApp.exe" )

Then, to make all the stuff work by accessing, say, http://localhost:8080/app/myApp.exe?p=a&..., I had to put an empty myApp.exe in lighttpd root folder (where the server's exe is). It's actually strange and sucks, and also not all CGIs can work that way. Applying these actions to another CGI app (that works perfectly on properly tuned Apache) gave no success.

What am I doing wrong?