diff --git a/src/broadcast.rs b/src/broadcast.rs
index 7351539..883ff6f 100644
--- a/src/broadcast.rs
+++ b/src/broadcast.rs
@@ -2,9 +2,10 @@
 //!
 //! The Reliable Broadcast Protocol assumes a network of `N` nodes that send signed messages to
 //! each other, with at most `f` of them faulty, where `3 * f < N`. Handling the networking and
-//! signing is the responsibility of this crate's user: only when a message has been verified to be
-//! "from node i", it can be handed to the `Broadcast` instance. One of the nodes is the "proposer"
-//! who sends a value. Under the above conditions, the protocol guarantees that either all or none
+//! signing is the responsibility of this crate's user; a message is only handed to the Broadcast
+//! instance after it has been verified to be "from node i". One of the nodes is the "proposer"
+//! who sends a value. It needs to be determined beforehand, and all nodes need to know and agree
+//! who it is. Under the above conditions, the protocol guarantees that either all or none
 //! of the correct nodes output a value, and that if the proposer is correct, all correct nodes
 //! output the proposed value.
 //!
@@ -19,15 +20,16 @@
 //! contains the `i`-th share of my value."
 //! * Every (correct) node that receives `Value(pi)` from the proposer sends it on to everyone else
 //! as `Echo(pi)`. An `Echo` translates to: "I have received `pi` directly from the proposer." If
-//! the proposer sends another `Value` message, that is ignored.
-//! * So every node that has received at least `f + 1` `Echo` messages with the same root
-//! hash will be able to decode a value.
+//! the proposer sends another `Value` message it is ignored.
+//! * So every node that receives at least `f + 1` `Echo` messages with the same root hash can
+//! decode a value.
 //! * Every node that has received `N - f` `Echo`s with the same root hash from different nodes
 //! knows that at least `f + 1` _correct_ nodes have sent an `Echo` with that hash to everyone, and
 //! therefore everyone will eventually receive at least `f + 1` of them. So upon receiving `N - f`
-//! `Echo`s, they send a `Ready(h)` to everyone to indicate that. `Ready` translates to: "I know
-//! that everyone will eventually be able to decode the value." Moreover, since every correct node
-//! only ever sends one kind of `Echo` message, this cannot happen for two different root hashes.
+//! `Echo`s, they send a `Ready(h)` to everyone. It translates to: "I know that everyone will
+//! eventually be able to decode the value with root hash `h`." Moreover, since every correct node
+//! only sends one kind of `Echo` message, there is no danger of receiving `N - f` `Echo`s with two
+//! different root hashes.
 //! * Even without enough `Echo` messages, if a node receives `f + 1` `Ready` messages, it knows
 //! that at least one _correct_ node has sent `Ready`. It therefore also knows that everyone will
 //! be able to decode eventually, and multicasts `Ready` itself.