How can I ignore noise from a flaky network connection?

My connection to the IRC server is often flaky, and I get disconnected and reconnected a lot. When this happens, I get a series of messages like this, repeated every time the connection flaps:

-!- Topic for #channel: Blah blah blah
-!- Topic set by nick [] [date, time, year]
[Users #channel]
[ nick] [ nick]
[ nick] [ nick]
-!- Irssi: #channel: Total of 4 nicks [0 ops, 0 halfops, 0 voices, 4 normal]
-!- Channel #channel created date, time, year
-!- Irssi: Join to #channel was synced in NN seconds

This floods the chat history with messages I don't actually care about. How can I hide them? If possible, I would like to not hide actual /topic changes (as opposed to the "you joined the channel" topic notification shown above).

I also get messages like this in the server tab, but I don't care as much about hiding them since there's rarely anything important in that tab:

-!- Irssi: No PONG reply from server irc.example.com in 301 seconds, disconnecting
-!- Irssi: Connection lost to irc.example.com
-!- Irssi: Removed reconnection to server irc.example.com port 1234
-!- Irssi: Looking up irc.example.com
-!- Irssi: Reconnecting to irc.example.com [192.0.2.123] port 1234 - use /RMRECONNS to abort
-!- Irssi: Connection to irc.example.com established
-!- Blah blah blah MOTD...
-!- End of /MOTD command.

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