Nginx's gzip static module

Which version? Nginx lists it as one of its standard modules, so it should be available to you:

http://wiki.nginx.org/Modules

If it isn't, you'll need to recompile. You can check the current list with 'nginx -V'

here is the output;

nginx: nginx version: nginx/1.0.10
nginx: TLS SNI support enabled
nginx: configure arguments: --prefix=/etc/nginx --conf-path=/etc/nginx/nginx.con      f --error-log-path=/var/log/nginx/error.log --http-client-body-temp-path=/var/li      b/nginx/body --http-fastcgi-temp-path=/var/lib/nginx/fastcgi --http-log-path=/va      r/log/nginx/access.log --http-proxy-temp-path=/var/lib/nginx/proxy --http-scgi-t      emp-path=/var/lib/nginx/scgi --http-uwsgi-temp-path=/var/lib/nginx/uwsgi --lock-      path=/var/lock/nginx.lock --pid-path=/var/run/nginx.pid --with-debug --with-http      _addition_module --with-http_dav_module --with-http_flv_module --with-http_geoip      _module --with-http_gzip_static_module --with-http_image_filter_module --with-ht      tp_mp4_module --with-http_perl_module --with-http_random_index_module --with-htt      p_realip_module --with-http_secure_link_module --with-http_stub_status_module --      with-http_ssl_module --with-http_sub_module --with-http_xslt_module --with-ipv6       --with-sha1=/usr/include/openssl --with-md5=/usr/include/openssl --with-mail --w      ith-mail_ssl_module --add-module=/build/buildd/nginx-1.0.10/debian/modules/nginx      -development-kit --add-module=/build/buildd/nginx-1.0.10/debian/modules/nginx-up      stream-fair --add-module=/build/buildd/nginx-1.0.10/debian/modules/nginx-echo --      add-module=/build/buildd/nginx-1.0.10/debian/modules/nginx-lua --add-module=/bui      ld/buildd/nginx-1.0.10/debian/modules/nginx-http-push --add-module=/build/buildd      /nginx-1.0.10/debian/modules/nginx-upload-progress --add-module=/build/buildd/ng      inx-1.0.10/debian/modules/chunkin-nginx-module --add-module=/build/buildd/nginx-      1.0.10/debian/modules/headers-more-nginx-module

does this means gzip static module is enabled?

That configure line contains "–with-httpgzipstatic_module", so I would guess yes?