Iptables – Dropping external connections to Docker container with iptables

I'm trying to set up iptables on a server running Docker containers.
Default rules generated by Docker set default policy to ACCEPT but I'd prefer to have it in a more restrictive manner: set default policy to DROP and expose to the Internet only specific ports (HTTP, SSH, etc).

I have an app container running with -p 0.0.0.0:8080:3000 as an upstream for nginx reverse proxy on port 80.

Here are iptables rules I currently have:

*nat
:PREROUTING ACCEPT [259:17205]
:INPUT ACCEPT [112:6660]
:OUTPUT ACCEPT [100:6000]
:POSTROUTING ACCEPT [45:2680]
:DOCKER - [0:0]
-A PREROUTING -m addrtype --dst-type LOCAL -j DOCKER
-A OUTPUT ! -d 127.0.0.0/8 -m addrtype --dst-type LOCAL -j DOCKER
-A POSTROUTING -s 172.17.0.0/16 ! -o docker0 -j MASQUERADE
-A POSTROUTING -s 172.17.0.4/32 -d 172.17.0.4/32 -p tcp -m tcp --dport 3000 -j MASQUERADE
-A POSTROUTING -s 172.17.0.4/32 -d 172.17.0.4/32 -p tcp -m tcp --dport 3000 -j MASQUERADE
-A POSTROUTING -s 172.17.0.4/32 -d 172.17.0.4/32 -p tcp -m tcp --dport 3000 -j MASQUERADE
-A POSTROUTING -s 172.17.0.4/32 -d 172.17.0.4/32 -p tcp -m tcp --dport 3000 -j MASQUERADE
-A POSTROUTING -s 172.17.0.4/32 -d 172.17.0.4/32 -p tcp -m tcp --dport 3000 -j MASQUERADE
-A DOCKER -i docker0 -j RETURN
-A DOCKER ! -i docker0 -p tcp -m tcp --dport 8080 -j DNAT --to-destination 172.17.0.4:3000
COMMIT
# Completed on Thu Feb 18 12:57:58 2016
# Generated by iptables-save v1.4.21 on Thu Feb 18 12:57:58 2016
*filter
:INPUT DROP [9:449]
:FORWARD DROP [0:0]
:OUTPUT DROP [5:300]
:DOCKER - [0:0]
:DOCKER-ISOLATION - [0:0]
-A INPUT -i lo -j ACCEPT
-A INPUT -p tcp -m tcp --dport 22 -m state --state NEW,ESTABLISHED -j ACCEPT
-A INPUT -p tcp -m tcp --sport 22 -m state --state ESTABLISHED -j ACCEPT
-A INPUT -p tcp -m state --state NEW,ESTABLISHED -m tcp --dport 2376 -j ACCEPT
-A INPUT -p tcp -m state --state NEW,ESTABLISHED -m tcp --dport 80 -j ACCEPT
-A INPUT -p tcp -m tcp --sport 80 -m state --state ESTABLISHED -j ACCEPT
-A INPUT -p tcp -m tcp --sport 443 -m state --state ESTABLISHED -j ACCEPT
-A INPUT -p udp -m udp --sport 53 -j ACCEPT
-A INPUT -p icmp -m icmp --icmp-type 8 -j ACCEPT
-A INPUT -p icmp -m icmp --icmp-type 0 -j ACCEPT
-A FORWARD -j DOCKER-ISOLATION
-A FORWARD -o docker0 -j DOCKER
-A FORWARD -o docker0 -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT
-A FORWARD -i docker0 ! -o docker0 -j ACCEPT
-A FORWARD -i docker0 -o docker0 -j ACCEPT
-A OUTPUT -o lo -j ACCEPT
-A OUTPUT -p tcp -m tcp --sport 22 -m state --state ESTABLISHED -j ACCEPT
-A OUTPUT -p tcp -m tcp --dport 22 -m state --state NEW,ESTABLISHED -j ACCEPT
-A OUTPUT -p tcp -m state --state ESTABLISHED -m tcp --sport 2376 -j ACCEPT
-A OUTPUT -p tcp -m state --state ESTABLISHED -m tcp --sport 80 -j ACCEPT
-A OUTPUT -p tcp -m tcp --dport 80 -m state --state NEW,ESTABLISHED -j ACCEPT
-A OUTPUT -p tcp -m tcp --dport 443 -m state --state NEW,ESTABLISHED -j ACCEPT
-A OUTPUT -p udp -m udp --dport 53 -j ACCEPT
-A OUTPUT -p icmp -m icmp --icmp-type 0 -j ACCEPT
-A OUTPUT -p icmp -m icmp --icmp-type 8 -j ACCEPT
-A DOCKER -d 172.17.0.4/32 ! -i docker0 -o docker0 -p tcp -m tcp --dport 3000 -j ACCEPT
-A DOCKER-ISOLATION -j RETURN
COMMIT

The problem is that they are too restrictive: nginx can't access the container.

I discovered that if I run:

iptables -I INPUT -i docker0 -j ACCEPT
iptables -I OUTPUT -o docker0 -j ACCEPT

it would work but also would made the container accessible from the Internet.

I tried adding -s 0.0.0.0 but it didn't help.

What am I doing wrong?