diff --git a/src/agreement/bin_values.rs b/src/agreement/bin_values.rs
index 11481d9..ac2b931 100644
--- a/src/agreement/bin_values.rs
+++ b/src/agreement/bin_values.rs
@@ -20,7 +20,7 @@ impl BinValues {
         replace(self, BinValues::None);
     }
 
-    fn from_bool(b: bool) -> Self {
+    pub fn from_bool(b: bool) -> Self {
         if b {
             BinValues::True
         } else {
diff --git a/src/agreement/mod.rs b/src/agreement/mod.rs
index 55c9f50..dc2e103 100644
--- a/src/agreement/mod.rs
+++ b/src/agreement/mod.rs
@@ -64,6 +64,14 @@ pub struct AgreementMessage {
     pub content: AgreementContent,
 }
 
+/// Possible values of the common coin schedule defining the method to derive the common coin in a
+/// given epoch: as a constant value or a distributed computation.
+enum CoinSchedule {
+    False,
+    True,
+    Random,
+}
+
 /// Binary Agreement instance
 pub struct Agreement<NodeUid> {
     /// Shared network information.
@@ -113,6 +121,8 @@ pub struct Agreement<NodeUid> {
     conf_round: bool,
     /// A common coin instance. It is reset on epoch update.
     common_coin: CommonCoin<NodeUid, Nonce>,
+    /// Common coin schedule computed at the start of each epoch.
+    coin_schedule: CoinSchedule,
 }
 
 impl<NodeUid: Clone + Debug + Ord> DistAlgorithm for Agreement<NodeUid> {
@@ -201,6 +211,7 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
                     netinfo,
                     Nonce::new(invocation_id.as_ref(), session_id, proposer_i, 0),
                 ),
+                coin_schedule: CoinSchedule::True,
             })
         } else {
             Err(ErrorKind::UnknownProposer.into())
@@ -252,9 +263,7 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
                 // Send an `Aux` message at most once per epoch.
                 self.send_aux(b)
             } else if bin_values_changed {
-                // If the `Conf` round has already started, a change in `bin_values` can lead to its
-                // end. Try if it has indeed finished.
-                self.try_finish_conf_round()
+                self.on_bin_values_changed()
             } else {
                 Ok(())
             }
@@ -267,6 +276,34 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
         }
     }
 
+    /// Called when `bin_values` changes as a result of receiving a `BVal` message. Tries to update
+    /// the epoch.
+    fn on_bin_values_changed(&mut self) -> AgreementResult<()> {
+        match self.coin_schedule {
+            CoinSchedule::False => {
+                let (aux_count, aux_vals) = self.count_aux();
+                if aux_count >= self.netinfo.num_nodes() - self.netinfo.num_faulty() {
+                    self.on_coin(false, aux_vals.definite())
+                } else {
+                    Ok(())
+                }
+            }
+            CoinSchedule::True => {
+                let (aux_count, aux_vals) = self.count_aux();
+                if aux_count >= self.netinfo.num_nodes() - self.netinfo.num_faulty() {
+                    self.on_coin(true, aux_vals.definite())
+                } else {
+                    Ok(())
+                }
+            }
+            CoinSchedule::Random => {
+                // If the `Conf` round has already started, a change in `bin_values` can lead to its
+                // end. Try if it has indeed finished.
+                self.try_finish_conf_round()
+            }
+        }
+    }
+
     fn send_bval(&mut self, b: bool) -> AgreementResult<()> {
         // Record the value `b` as sent.
         self.sent_bval.insert(b);
@@ -309,12 +346,21 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
         if self.bin_values == BinValues::None {
             return Ok(());
         }
-        if self.count_aux() < self.netinfo.num_nodes() - self.netinfo.num_faulty() {
+        let (aux_count, aux_vals) = self.count_aux();
+        if aux_count < self.netinfo.num_nodes() - self.netinfo.num_faulty() {
             // Continue waiting for the (N - f) `Aux` messages.
             return Ok(());
         }
-        // Start the `Conf` message round.
-        self.send_conf()
+
+        // Execute the Common Coin schedule `false, true, get_coin(), false, true, get_coin(), ...`
+        match self.coin_schedule {
+            CoinSchedule::False => self.on_coin(false, aux_vals.definite()),
+            CoinSchedule::True => self.on_coin(true, aux_vals.definite()),
+            CoinSchedule::Random => {
+                // Start the `Conf` message round.
+                self.send_conf()
+            }
+        }
     }
 
     fn handle_conf(&mut self, sender_id: &NodeUid, v: BinValues) -> AgreementResult<()> {
@@ -344,29 +390,47 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
         self.extend_common_coin();
 
         if let Some(coin) = self.common_coin.next_output() {
-            let b = if let Some(b) = self.count_conf().1.definite() {
-                // Outputting a value is allowed only once.
-                if self.decision.is_none() && b == coin {
-                    self.decide(b);
-                }
-                b
-            } else {
-                coin
-            };
+            let def_bin_value = self.count_conf().1.definite();
+            self.on_coin(coin, def_bin_value)?;
+        }
 
-            self.start_next_epoch();
+        Ok(())
+    }
 
-            self.estimated = Some(b);
-            self.send_bval(b)?;
-            let queued_msgs = replace(&mut self.incoming_queue, Vec::new());
-            for (sender_id, msg) in queued_msgs {
-                self.handle_message(&sender_id, msg)?;
+    /// When the common coin has been computed, tries to decide on an output value, updates the
+    /// `Agreement` epoch and handles queued messages for the new epoch.
+    fn on_coin(&mut self, coin: bool, def_bin_value: Option<bool>) -> AgreementResult<()> {
+        let b = if let Some(b) = def_bin_value {
+            // Outputting a value is allowed only once.
+            if self.decision.is_none() && b == coin {
+                self.decide(b);
             }
+            b
+        } else {
+            coin
+        };
+
+        self.update_epoch();
+
+        self.estimated = Some(b);
+        self.send_bval(b)?;
+        let queued_msgs = replace(&mut self.incoming_queue, Vec::new());
+        for (sender_id, msg) in queued_msgs {
+            self.handle_message(&sender_id, msg)?;
         }
         Ok(())
     }
 
-    // Propagates Common Coin messages to the top level.
+    /// Computes the coin schedule for the current `Agreement` epoch.
+    fn coin_schedule(&self) -> CoinSchedule {
+        match self.epoch % 3 {
+            0 => CoinSchedule::True,
+            1 => CoinSchedule::False,
+            _ => CoinSchedule::Random,
+        }
+    }
+
+    /// Propagates Common Coin messages to the top level.
     fn extend_common_coin(&mut self) {
         let epoch = self.epoch;
         self.messages.extend(self.common_coin.message_iter().map(
@@ -423,7 +487,7 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
     /// In general, we can't expect every good node to send the same `Aux` value, so waiting for N -
     /// f agreeing messages would not always terminate. We can, however, expect every good node to
     /// send an `Aux` value that will eventually end up in our `bin_values`.
-    fn count_aux(&self) -> usize {
+    fn count_aux(&self) -> (usize, BinValues) {
         let mut aux: BTreeMap<_, _> = self
             .received_aux
             .iter()
@@ -438,7 +502,8 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
 
         // Ensure that nodes are not counted twice.
         aux.extend(term);
-        aux.len()
+        let bin: BinValues = aux.values().map(|&&v| BinValues::from_bool(v)).collect();
+        (aux.len(), bin)
     }
 
     /// Counts the number of received `Conf` messages.
@@ -452,7 +517,7 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
         (vals_cnt.count(), vals.cloned().collect())
     }
 
-    fn start_next_epoch(&mut self) {
+    fn update_epoch(&mut self) {
         self.bin_values.clear();
         self.received_bval.clear();
         self.sent_bval.clear();
@@ -466,7 +531,10 @@ impl<NodeUid: Clone + Debug + Ord> Agreement<NodeUid> {
             *self.netinfo.node_index(&self.proposer_id).unwrap(),
             self.epoch,
         );
+        // TODO: Don't spend time creating a `CommonCoin` instance in epochs where the common coin
+        // is known.
         self.common_coin = CommonCoin::new(self.netinfo.clone(), nonce);
+        self.coin_schedule = self.coin_schedule();
         debug!(
             "{:?} Agreement instance {:?} started epoch {}",
             self.netinfo.our_uid(),