Simple port forwarding with iptables

I start with the following which doesn't seem necessary, but it doesn't seem to hurt:

echo 1 | sudo tee /proc/sys/net/ipv4/ip_forward

The following two commands create port forwarding from port 5433 to port 5432.

sudo /sbin/iptables -t nat -A PREROUTING -i eth0 -p tcp -m tcp --dport 5433 -m comment --comment "Port forward 5433->5432" -j REDIRECT --to-ports 5432
sudo /sbin/iptables -t nat -A OUTPUT -s 127.0.0.1/32 -p tcp -m tcp --dport 5433 -m comment --comment "Port forward 5433->5432" -j REDIRECT --to-ports 5432

This works locally. Both of the following commands successfully connect and get "Empty reply" because the listening server is not HTTP.

curl http://localhost:5432
curl http://localhost:5433

However, when I run the same commands from another server:

curl http://<local IP>:5432
curl http://<local IP>:5433

The 5432 curl connects, but the 5433 curl does not, which means the port forwarding doesn't seem to work from a remote server.

How can I fix my iptables rules to make port forwarding work from remote servers as well as local servers?

I see the second rule specifies a "source" IP of 127.0.0.1/32. I tried changing this and couldn't find something that worked.