diff --git a/linera-chain/src/outbox.rs b/linera-chain/src/outbox.rs
index 9043796301d..593f2c82075 100644
--- a/linera-chain/src/outbox.rs
+++ b/linera-chain/src/outbox.rs
@@ -6,7 +6,7 @@ use linera_base::data_types::{ArithmeticError, BlockHeight};
 use linera_views::context::{create_test_memory_context, MemoryContext};
 use linera_views::{
     context::Context,
-    queue_view::QueueView,
+    bucket_queue_view::BucketQueueView,
     register_view::RegisterView,
     views::{ClonableView, View, ViewError},
 };
@@ -15,6 +15,12 @@ use linera_views::{
 #[path = "unit_tests/outbox_tests.rs"]
 mod outbox_tests;
 
+// The number of block heights in a bucket
+// The `BlockHeight` has just 8 bytes so the size is constant.
+// This means that by choosing a size of 1000, we have a
+// reasonable size that will not create any memory issues.
+const BLOCKHEIGHT_BUCKET_SIZE: usize = 1000;
+
 /// The state of an outbox
 /// * An outbox is used to send messages to another chain.
 /// * Internally, this is implemented as a FIFO queue of (increasing) block heights.
@@ -31,7 +37,7 @@ where
     pub next_height_to_schedule: RegisterView<C, BlockHeight>,
     /// Keep sending these certified blocks of ours until they are acknowledged by
     /// receivers.
-    pub queue: QueueView<C, BlockHeight>,
+    pub queue: BucketQueueView<C, BlockHeight, BLOCKHEIGHT_BUCKET_SIZE>,
 }
 
 impl<C> OutboxStateView<C>
@@ -59,11 +65,11 @@ where
         height: BlockHeight,
     ) -> Result<Vec<BlockHeight>, ViewError> {
         let mut updates = Vec::new();
-        while let Some(h) = self.queue.front().await? {
+        while let Some(h) = self.queue.front().cloned() {
             if h > height {
                 break;
             }
-            self.queue.delete_front();
+            self.queue.delete_front().await?;
             updates.push(h);
         }
         Ok(updates)
diff --git a/linera-core/src/chain_worker/state/mod.rs b/linera-core/src/chain_worker/state/mod.rs
index 7ba248ee712..de56d737c6f 100644
--- a/linera-core/src/chain_worker/state/mod.rs
+++ b/linera-core/src/chain_worker/state/mod.rs
@@ -530,8 +530,8 @@ where
         let outboxes = self.chain.outboxes.try_load_entries(&targets).await?;
         for outbox in outboxes {
             let outbox = outbox.expect("Only existing outboxes should be referenced by `indices`");
-            let front = outbox.queue.front().await?;
-            if front.is_some_and(|key| key <= height) {
+            let front = outbox.queue.front();
+            if front.is_some_and(|key| *key <= height) {
                 return Ok(false);
             }
         }