  Paxos, the de facto standard approach to solving distributed consensus,
operates in two phases, each of which requires an intersecting quorum of nodes.
Multi-Paxos reduces this to one phase by electing a leader but this leader is
also a performance bottleneck. Fast Paxos bypasses the leader but has stronger
quorum intersection requirements.
  In this paper we observe that Fast Paxos' intersection requirements can be
safely relaxed, reducing to just one additional intersection requirement
between phase-1 quorums and any pair of fast round phase-2 quorums. We thus
find that the quorums used with Fast Paxos are larger than necessary, allowing
alternative quorum systems to obtain new tradeoffs between performance and
fault-tolerance.
