how to enable gzip compression in custom app when using https?

I have a custom application which communicates with mobile devices using json. Using gzip compression has a significant impact on network performance since it reduces file sizes by 60-70%. However, I've found that gzip compression is only working on the http version, not https.

I used a tool at http://checkgzipcompression.com/ to verify this, and curl shows the same results. I don't think that I have control over the configuration of nginx which is proxying my application. Is there anything that I can do to get gzip compression on https?

Details below:

curl -v -H 'Accept-Encoding: gzip' http://...

> Accept-Encoding: gzip
< HTTP/1.1 200 OK
< Server: nginx
< Date: Mon, 09 Sep 2013 06:21:27 GMT
< Content-Type: application/json; charset=utf-8
< Transfer-Encoding: chunked
< Connection: keep-alive
< Vary: Accept-Encoding
< Pragma: no-cache
< Cache-Control: no-cache
< Content-Encoding: gzip

curl -v -H 'Accept-Encoding: gzip' https://...

> Accept-Encoding: gzip
< HTTP/1.1 200 OK
< Server: nginx
< Date: Mon, 09 Sep 2013 06:28:19 GMT
< Content-Type: application/json; charset=utf-8
< Content-Length: 794957
< Connection: keep-alive
< Pragma: no-cache
< Cache-Control: no-cache