Nginx 1.4.4-4 / limit_conn / limit rate

Dear honorable members,

I switched recently from Apache / Debian to Nginx / Debian and
i'm struggling a bit right now. I hope to find some help in this forum.

System info:
Nginx-Full 1.4.4-4 / Debian Jessie

Goal:
Limit the connections per IP to 1 with a limited bandwith (20 Megabit/s) for every connection.

Done so far:
nginx.conf:
limit_conn_zone $binary_remote_addr zone=addr:10m;

in the location block:
limit_conn addr 1;
limit_rate 2621440;

I see a lot of entries in the error.log looking like this:

limiting connections by zone addr ...

I assume, that the limit_conn is working, but people are still downloading with 100 MBit/s or more. Im stuck and would really appreciate some advice.

Thank you in advance.