diff --git a/Cargo.lock b/Cargo.lock
index c31e3f0..a5dc428 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -492,6 +492,7 @@ dependencies = [
  "serde_asn1_der",
  "serde_json",
  "signature",
+ "tinyvec",
  "tracing",
 ]
 
@@ -934,6 +935,22 @@ dependencies = [
  "serde_json",
 ]
 
+[[package]]
+name = "tinyvec"
+version = "1.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "445e881f4f6d382d5f27c034e25eb92edd7c784ceab92a0937db7f2e9471b938"
+dependencies = [
+ "serde",
+ "tinyvec_macros",
+]
+
+[[package]]
+name = "tinyvec_macros"
+version = "0.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1f3ccbac311fea05f86f61904b462b55fb3df8837a366dfc601a0161d0532f20"
+
 [[package]]
 name = "tokio"
 version = "1.40.0"
diff --git a/manul/Cargo.toml b/manul/Cargo.toml
index 893157b..ede1380 100644
--- a/manul/Cargo.toml
+++ b/manul/Cargo.toml
@@ -20,6 +20,7 @@ rand_core = { version = "0.6.4", default-features = false }
 tracing = { version = "0.1", default-features = false }
 displaydoc = { version = "0.2", default-features = false }
 derive-where = "1"
+tinyvec = { version = "1", default-features = false, features = ["alloc", "serde"] }
 
 rand = { version = "0.8", default-features = false, optional = true }
 serde-persistent-deserializer = { version = "0.3", optional = true }
diff --git a/manul/src/protocol/round.rs b/manul/src/protocol/round.rs
index 794677c..bf6f6e7 100644
--- a/manul/src/protocol/round.rs
+++ b/manul/src/protocol/round.rs
@@ -3,6 +3,7 @@ use alloc::{
     collections::{BTreeMap, BTreeSet},
     format,
     string::String,
+    vec,
     vec::Vec,
 };
 use core::{
@@ -12,6 +13,7 @@ use core::{
 
 use rand_core::CryptoRngCore;
 use serde::{Deserialize, Serialize};
+use tinyvec::{tiny_vec, TinyVec};
 
 use super::{
     errors::{FinalizeError, LocalError, MessageValidationError, ProtocolValidationError, ReceiveError},
@@ -29,24 +31,18 @@ pub enum FinalizeOutcome<Id: PartyId, P: Protocol> {
     Result(P::Result),
 }
 
-// Maximum depth of group nesting in RoundIds.
-// We need this to be limited to allow the nesting to be performed in `const` context
-// (since we cannot use heap there).
-const ROUND_ID_DEPTH: usize = 8;
-
 /// A round identifier.
-#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Serialize, Deserialize)]
+#[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Serialize, Deserialize)]
 pub struct RoundId {
-    depth: u8,
-    round_nums: [u8; ROUND_ID_DEPTH],
+    round_nums: TinyVec<[u8; 4]>,
     is_echo: bool,
 }
 
 impl Display for RoundId {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
         write!(f, "Round ")?;
-        for i in (0..self.depth as usize).rev() {
-            write!(f, "{}", self.round_nums.get(i).expect("Depth within range"))?;
+        for (i, round_num) in self.round_nums.iter().enumerate().rev() {
+            write!(f, "{}", round_num)?;
             if i != 0 {
                 write!(f, "-")?;
             }
@@ -60,36 +56,18 @@ impl Display for RoundId {
 
 impl RoundId {
     /// Creates a new round identifier.
-    pub const fn new(round_num: u8) -> Self {
-        let mut round_nums = [0u8; ROUND_ID_DEPTH];
-        #[allow(clippy::indexing_slicing)]
-        {
-            round_nums[0] = round_num;
-        }
+    pub fn new(round_num: u8) -> Self {
         Self {
-            depth: 1,
-            round_nums,
+            round_nums: tiny_vec!(round_num, 0, 0, 0),
             is_echo: false,
         }
     }
 
     /// Prefixes this round ID (possibly already nested) with a group number.
-    ///
-    /// **Warning:** the maximum nesting depth is 8. Panics if this nesting overflows it.
-    pub(crate) const fn group_under(&self, round_num: u8) -> Self {
-        if self.depth as usize == ROUND_ID_DEPTH {
-            panic!("Maximum depth reached");
-        }
-        let mut round_nums = self.round_nums;
-
-        // Would use `expect("Depth within range")` here, but `expect()` in const fns is unstable.
-        #[allow(clippy::indexing_slicing)]
-        {
-            round_nums[self.depth as usize] = round_num;
-        }
-
+    pub(crate) fn group_under(&self, round_num: u8) -> Self {
+        let mut round_nums = self.round_nums.clone();
+        round_nums.push(round_num);
         Self {
-            depth: self.depth + 1,
             round_nums,
             is_echo: self.is_echo,
         }
@@ -99,13 +77,12 @@ impl RoundId {
     ///
     /// Returns the `Err` variant if the round ID is not nested.
     pub(crate) fn ungroup(&self) -> Result<Self, LocalError> {
-        if self.depth == 1 {
+        if self.round_nums.len() == 1 {
             Err(LocalError::new("This round ID is not in a group"))
         } else {
-            let mut round_nums = self.round_nums;
-            *round_nums.get_mut(self.depth as usize - 1).expect("Depth within range") = 0;
+            let mut round_nums = self.round_nums.clone();
+            round_nums.pop().expect("vector size greater than 1");
             Ok(Self {
-                depth: self.depth - 1,
                 round_nums,
                 is_echo: self.is_echo,
             })
@@ -127,8 +104,7 @@ impl RoundId {
             panic!("This is already an echo round ID");
         }
         Self {
-            depth: self.depth,
-            round_nums: self.round_nums,
+            round_nums: self.round_nums.clone(),
             is_echo: true,
         }
     }
@@ -143,8 +119,7 @@ impl RoundId {
             panic!("This is already an non-echo round ID");
         }
         Self {
-            depth: self.depth,
-            round_nums: self.round_nums,
+            round_nums: self.round_nums.clone(),
             is_echo: false,
         }
     }
diff --git a/manul/src/session/evidence.rs b/manul/src/session/evidence.rs
index c0fab32..eafd75c 100644
--- a/manul/src/session/evidence.rs
+++ b/manul/src/session/evidence.rs
@@ -100,8 +100,8 @@ where
             .iter()
             .map(|round_id| {
                 transcript
-                    .get_echo_broadcast(*round_id, verifier)
-                    .map(|echo| (*round_id, echo))
+                    .get_echo_broadcast(round_id.clone(), verifier)
+                    .map(|echo| (round_id.clone(), echo))
             })
             .collect::<Result<BTreeMap<_, _>, _>>()?;
 
@@ -110,8 +110,8 @@ where
             .iter()
             .map(|round_id| {
                 transcript
-                    .get_normal_broadcast(*round_id, verifier)
-                    .map(|bc| (*round_id, bc))
+                    .get_normal_broadcast(round_id.clone(), verifier)
+                    .map(|bc| (round_id.clone(), bc))
             })
             .collect::<Result<BTreeMap<_, _>, _>>()?;
 
@@ -120,8 +120,8 @@ where
             .iter()
             .map(|round_id| {
                 transcript
-                    .get_direct_message(*round_id, verifier)
-                    .map(|dm| (*round_id, dm))
+                    .get_direct_message(round_id.clone(), verifier)
+                    .map(|dm| (round_id.clone(), dm))
             })
             .collect::<Result<BTreeMap<_, _>, _>>()?;
 
@@ -131,7 +131,7 @@ where
             .map(|round_id| {
                 transcript
                     .get_normal_broadcast(round_id.echo(), verifier)
-                    .map(|dm| (*round_id, dm))
+                    .map(|dm| (round_id.clone(), dm))
             })
             .collect::<Result<BTreeMap<_, _>, _>>()?;
 
@@ -470,12 +470,12 @@ where
         for (round_id, direct_message) in self.direct_messages.iter() {
             let verified_direct_message = direct_message.clone().verify::<SP>(verifier)?;
             let metadata = verified_direct_message.metadata();
-            if metadata.session_id() != session_id || metadata.round_id() != *round_id {
+            if metadata.session_id() != session_id || &metadata.round_id() != round_id {
                 return Err(EvidenceError::InvalidEvidence(
                     "Invalid attached message metadata".into(),
                 ));
             }
-            verified_direct_messages.insert(*round_id, verified_direct_message.payload().clone());
+            verified_direct_messages.insert(round_id.clone(), verified_direct_message.payload().clone());
         }
 
         let verified_echo_broadcast = self.echo_broadcast.clone().verify::<SP>(verifier)?.payload().clone();
@@ -500,31 +500,31 @@ where
         for (round_id, echo_broadcast) in self.echo_broadcasts.iter() {
             let verified_echo_broadcast = echo_broadcast.clone().verify::<SP>(verifier)?;
             let metadata = verified_echo_broadcast.metadata();
-            if metadata.session_id() != session_id || metadata.round_id() != *round_id {
+            if metadata.session_id() != session_id || &metadata.round_id() != round_id {
                 return Err(EvidenceError::InvalidEvidence(
                     "Invalid attached message metadata".into(),
                 ));
             }
-            verified_echo_broadcasts.insert(*round_id, verified_echo_broadcast.payload().clone());
+            verified_echo_broadcasts.insert(round_id.clone(), verified_echo_broadcast.payload().clone());
         }
 
         let mut verified_normal_broadcasts = BTreeMap::new();
         for (round_id, normal_broadcast) in self.normal_broadcasts.iter() {
             let verified_normal_broadcast = normal_broadcast.clone().verify::<SP>(verifier)?;
             let metadata = verified_normal_broadcast.metadata();
-            if metadata.session_id() != session_id || metadata.round_id() != *round_id {
+            if metadata.session_id() != session_id || &metadata.round_id() != round_id {
                 return Err(EvidenceError::InvalidEvidence(
                     "Invalid attached message metadata".into(),
                 ));
             }
-            verified_normal_broadcasts.insert(*round_id, verified_normal_broadcast.payload().clone());
+            verified_normal_broadcasts.insert(round_id.clone(), verified_normal_broadcast.payload().clone());
         }
 
         let mut combined_echos = BTreeMap::new();
         for (round_id, combined_echo) in self.combined_echos.iter() {
             let verified_combined_echo = combined_echo.clone().verify::<SP>(verifier)?;
             let metadata = verified_combined_echo.metadata();
-            if metadata.session_id() != session_id || metadata.round_id().non_echo() != *round_id {
+            if metadata.session_id() != session_id || &metadata.round_id().non_echo() != round_id {
                 return Err(EvidenceError::InvalidEvidence(
                     "Invalid attached message metadata".into(),
                 ));
@@ -537,14 +537,14 @@ where
             for (other_verifier, echo_broadcast) in echo_set.echo_broadcasts.iter() {
                 let verified_echo_broadcast = echo_broadcast.clone().verify::<SP>(other_verifier)?;
                 let metadata = verified_echo_broadcast.metadata();
-                if metadata.session_id() != session_id || metadata.round_id() != *round_id {
+                if metadata.session_id() != session_id || &metadata.round_id() != round_id {
                     return Err(EvidenceError::InvalidEvidence(
                         "Invalid attached message metadata".into(),
                     ));
                 }
                 verified_echo_set.push(verified_echo_broadcast.payload().clone());
             }
-            combined_echos.insert(*round_id, verified_echo_set);
+            combined_echos.insert(round_id.clone(), verified_echo_set);
         }
 
         Ok(self.error.verify_messages_constitute_error(
diff --git a/manul/src/session/message.rs b/manul/src/session/message.rs
index 51dbc55..199c2f0 100644
--- a/manul/src/session/message.rs
+++ b/manul/src/session/message.rs
@@ -68,7 +68,7 @@ impl MessageMetadata {
     }
 
     pub fn round_id(&self) -> RoundId {
-        self.round_id
+        self.round_id.clone()
     }
 }
 
diff --git a/manul/src/session/session.rs b/manul/src/session/session.rs
index b8edb31..db81183 100644
--- a/manul/src/session/session.rs
+++ b/manul/src/session/session.rs
@@ -317,7 +317,7 @@ where
             }
             MessageFor::ThisRound
         } else if self.possible_next_rounds.contains(&message_round_id) {
-            if accum.message_is_cached(from, message_round_id) {
+            if accum.message_is_cached(from, &message_round_id) {
                 let err = format!("Message for {:?} is already cached", message_round_id);
                 accum.register_unprovable_error(from, RemoteError::new(&err))?;
                 trace!("{key:?} {err}");
@@ -354,7 +354,7 @@ where
         match message_for {
             MessageFor::ThisRound => {
                 accum.mark_processing(&verified_message)?;
-                Ok(PreprocessOutcome::ToProcess(verified_message))
+                Ok(PreprocessOutcome::ToProcess(Box::new(verified_message)))
             }
             MessageFor::NextRound => {
                 debug!("{key:?}: Caching message from {from:?} for {message_round_id}");
@@ -406,7 +406,7 @@ where
     ) -> Result<SessionReport<P, SP>, LocalError> {
         let round_id = self.round_id();
         let transcript = self.transcript.update(
-            round_id,
+            &round_id,
             accum.echo_broadcasts,
             accum.normal_broadcasts,
             accum.direct_messages,
@@ -446,7 +446,7 @@ where
         let round_id = self.round_id();
 
         let transcript = self.transcript.update(
-            round_id,
+            &round_id,
             accum.echo_broadcasts,
             accum.normal_broadcasts,
             accum.direct_messages,
@@ -604,9 +604,9 @@ where
         self.processing.contains(from)
     }
 
-    fn message_is_cached(&self, from: &SP::Verifier, round_id: RoundId) -> bool {
+    fn message_is_cached(&self, from: &SP::Verifier, round_id: &RoundId) -> bool {
         if let Some(entry) = self.cached.get(from) {
-            entry.contains_key(&round_id)
+            entry.contains_key(round_id)
         } else {
             false
         }
@@ -745,7 +745,7 @@ where
         let from = message.from().clone();
         let round_id = message.metadata().round_id();
         let cached = self.cached.entry(from.clone()).or_default();
-        if cached.insert(round_id, message).is_some() {
+        if cached.insert(round_id.clone(), message).is_some() {
             return Err(LocalError::new(format!(
                 "A message from for {:?} has already been cached",
                 round_id
@@ -771,7 +771,7 @@ pub struct ProcessedMessage<P: Protocol, SP: SessionParameters> {
 #[derive(Debug, Clone)]
 pub enum PreprocessOutcome<Verifier> {
     /// The message was successfully verified, pass it on to [`Session::process_message`].
-    ToProcess(VerifiedMessage<Verifier>),
+    ToProcess(Box<VerifiedMessage<Verifier>>),
     /// The message was intended for the next round and was cached.
     ///
     /// No action required now, cached messages will be returned on successful [`Session::finalize_round`].
@@ -795,7 +795,7 @@ impl<Verifier> PreprocessOutcome<Verifier> {
     /// so the user may choose to ignore them if no logging is desired.
     pub fn ok(self) -> Option<VerifiedMessage<Verifier>> {
         match self {
-            Self::ToProcess(message) => Some(message),
+            Self::ToProcess(message) => Some(*message),
             _ => None,
         }
     }
diff --git a/manul/src/session/transcript.rs b/manul/src/session/transcript.rs
index 382448d..3f678e5 100644
--- a/manul/src/session/transcript.rs
+++ b/manul/src/session/transcript.rs
@@ -36,7 +36,7 @@ where
     #[allow(clippy::too_many_arguments)]
     pub fn update(
         self,
-        round_id: RoundId,
+        round_id: &RoundId,
         echo_broadcasts: BTreeMap<SP::Verifier, SignedMessagePart<EchoBroadcast>>,
         normal_broadcasts: BTreeMap<SP::Verifier, SignedMessagePart<NormalBroadcast>>,
         direct_messages: BTreeMap<SP::Verifier, SignedMessagePart<DirectMessage>>,
@@ -45,7 +45,7 @@ where
         missing_messages: BTreeSet<SP::Verifier>,
     ) -> Result<Self, LocalError> {
         let mut all_echo_broadcasts = self.echo_broadcasts;
-        match all_echo_broadcasts.entry(round_id) {
+        match all_echo_broadcasts.entry(round_id.clone()) {
             Entry::Vacant(entry) => entry.insert(echo_broadcasts),
             Entry::Occupied(_) => {
                 return Err(LocalError::new(format!(
@@ -55,7 +55,7 @@ where
         };
 
         let mut all_normal_broadcasts = self.normal_broadcasts;
-        match all_normal_broadcasts.entry(round_id) {
+        match all_normal_broadcasts.entry(round_id.clone()) {
             Entry::Vacant(entry) => entry.insert(normal_broadcasts),
             Entry::Occupied(_) => {
                 return Err(LocalError::new(format!(
@@ -65,7 +65,7 @@ where
         };
 
         let mut all_direct_messages = self.direct_messages;
-        match all_direct_messages.entry(round_id) {
+        match all_direct_messages.entry(round_id.clone()) {
             Entry::Vacant(entry) => entry.insert(direct_messages),
             Entry::Occupied(_) => {
                 return Err(LocalError::new(format!(
@@ -93,7 +93,7 @@ where
         }
 
         let mut all_missing_messages = self.missing_messages;
-        match all_missing_messages.entry(round_id) {
+        match all_missing_messages.entry(round_id.clone()) {
             Entry::Vacant(entry) => entry.insert(missing_messages),
             Entry::Occupied(_) => {
                 return Err(LocalError::new(format!(