diff --git a/fastcrypto-tbls/src/nodes.rs b/fastcrypto-tbls/src/nodes.rs
index 149f02eebb..71e01caec3 100644
--- a/fastcrypto-tbls/src/nodes.rs
+++ b/fastcrypto-tbls/src/nodes.rs
@@ -8,6 +8,7 @@ use fastcrypto::error::{FastCryptoError, FastCryptoResult};
 use fastcrypto::groups::GroupElement;
 use fastcrypto::hash::{Blake2b256, Digest, HashFunction};
 use serde::{Deserialize, Serialize};
+use tracing::debug;
 
 pub type PartyId = u16;
 
@@ -145,14 +146,28 @@ impl<G: GroupElement + Serialize> Nodes<G> {
     /// - The precision loss, counted as the sum of the remainders of the division by d, is at most
     ///   the allowed delta
     /// In practice, allowed delta will be the extra liveness we would assume above 2f+1.
-    pub fn reduce(&self, t: u16, allowed_delta: u16) -> (Self, u16) {
+    /// total_weight_lower_bound allows limiting the level of reduction (e.g., in benchmarks). To get the best results,
+    /// set it to 1.
+    pub fn reduce(&self, t: u16, allowed_delta: u16, total_weight_lower_bound: u32) -> (Self, u16) {
+        assert!(total_weight_lower_bound <= self.total_weight && total_weight_lower_bound > 0);
         let mut max_d = 1;
         for d in 2..=40 {
-            let sum = self.nodes.iter().map(|n| n.weight % d).sum::<u16>();
-            if sum <= allowed_delta {
+            // Break if we reached the lower bound.
+            let new_total_weight = self.nodes.iter().map(|n| n.weight / d).sum::<u16>();
+            if new_total_weight < total_weight_lower_bound as u16 {
+                break;
+            }
+            // Compute the precision loss.
+            let delta = self.nodes.iter().map(|n| n.weight % d).sum::<u16>();
+            if delta <= allowed_delta {
                 max_d = d;
             }
         }
+        debug!(
+            "Nodes::reduce reducing from {} with max_d {}, allowed_delta {}, total_weight_lower_bound {}",
+            self.total_weight, max_d, allowed_delta, total_weight_lower_bound
+        );
+
         let nodes = self
             .nodes
             .iter()
diff --git a/fastcrypto-tbls/src/tests/nodes_tests.rs b/fastcrypto-tbls/src/tests/nodes_tests.rs
index 11b2c97d0b..90958633dd 100644
--- a/fastcrypto-tbls/src/tests/nodes_tests.rs
+++ b/fastcrypto-tbls/src/tests/nodes_tests.rs
@@ -188,12 +188,12 @@ fn test_reduce() {
         let t = (nodes.total_weight() / 3) as u16;
 
         // No extra gap, should return the inputs
-        let (new_nodes, new_t) = nodes.reduce(t, 1);
+        let (new_nodes, new_t) = nodes.reduce(t, 1, 1);
         assert_eq!(nodes, new_nodes);
         assert_eq!(t, new_t);
 
         // 10% gap
-        let (new_nodes, _new_t) = nodes.reduce(t, (nodes.total_weight() / 10) as u16);
+        let (new_nodes, _new_t) = nodes.reduce(t, (nodes.total_weight() / 10) as u16, 1);
         // Estimate the real factor d
         let d = nodes.iter().last().unwrap().weight / new_nodes.iter().last().unwrap().weight;
         // The loss per node is on average (d - 1) / 2
@@ -201,3 +201,27 @@ fn test_reduce() {
         assert!((d - 1) / 2 * number_of_nodes < ((nodes.total_weight() / 9) as u16));
     }
 }
+
+#[test]
+fn test_reduce_with_lower_bounds() {
+    let number_of_nodes = 100;
+    let node_vec = get_nodes::<RistrettoPoint>(number_of_nodes);
+    let nodes = Nodes::new(node_vec).unwrap();
+    let t = (nodes.total_weight() / 3) as u16;
+
+    // No extra gap, should return the inputs
+    let (new_nodes, new_t) = nodes.reduce(t, 1, 1);
+    assert_eq!(nodes, new_nodes);
+    assert_eq!(t, new_t);
+
+    // 10% gap
+    let (new_nodes1, _new_t1) = nodes.reduce(t, (nodes.total_weight() / 20) as u16, 1);
+    let (new_nodes2, _new_t2) = nodes.reduce(
+        t,
+        (nodes.total_weight() / 20) as u16,
+        nodes.total_weight() / 3,
+    );
+    assert!(new_nodes1.total_weight() < new_nodes2.total_weight());
+    assert!(new_nodes2.total_weight() >= nodes.total_weight() / 3);
+    assert!(new_nodes2.total_weight() < nodes.total_weight());
+}