double Nat
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There's nothing theoretically bad about a double-NAT connection.
Since it's a slightly more complicated networking topology, it
may bring some bugs in your router, modem, etc. to the surface,
but apart from that, there's nothing else bad about it. The performance
impact is negligible. Personally, I try to avoid double-NAT'S, but there's many situations you just can't get around. DSL's are the #1 example.
DSL providers are migrating/already migrated to a combined DSL modem/
router unit which does the PPPoE termination, so it's a DHCP-able
straight ethernet output which'll plug directly into your PC without the
need for special DSL software. Some of these units have limitations on
their DHCP, etc, so you have to add an additional router in a double-NAT
config. No way around it. Yes, I've tried setting up routers in a non-router/bridge mode (use router as switch only: don't use Internet port,
disable DHCP, or play with router's IP/subnet address), and this
sometimes works and sometimes doesn't.
QoS
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Most low-end routers, like the ones most people buy, don't have any
QoS settings.