diff --git a/pageserver/src/layered_repository/inmemory_layer.rs b/pageserver/src/layered_repository/inmemory_layer.rs
index 154954a9dc..4554f58589 100644
--- a/pageserver/src/layered_repository/inmemory_layer.rs
+++ b/pageserver/src/layered_repository/inmemory_layer.rs
@@ -775,12 +775,7 @@ impl InMemoryLayer {
 
         let end_lsn = self.end_lsn.unwrap();
 
-        let mut before_segsizes = OrderedVec::default();
-        for (lsn, size) in inner.segsizes.iter() {
-            if *lsn <= end_lsn {
-                before_segsizes.append(*lsn, *size);
-            }
-        }
+        let before_segsizes = inner.segsizes.copy_prefix(&Lsn(end_lsn.0 + 1));
         let mut before_page_versions = inner.page_versions.ordered_iter(Some(end_lsn));
 
         let mut frozen_layers: Vec<Arc<dyn Layer>> = Vec::new();
diff --git a/zenith_utils/src/ordered_vec.rs b/zenith_utils/src/ordered_vec.rs
index 8d3c46afd0..dbef45bd23 100644
--- a/zenith_utils/src/ordered_vec.rs
+++ b/zenith_utils/src/ordered_vec.rs
@@ -91,6 +91,19 @@ impl<K: Ord + Copy, V> OrderedVec<K, V> {
         self.0.is_empty()
     }
 
+    pub fn copy_prefix(&self, key: &K) -> Self
+    where
+        K: Clone,
+        V: Clone,
+    {
+        let idx = match self.0.binary_search_by_key(key, extract_key) {
+            Ok(idx) => idx,
+            Err(idx) => idx,
+        };
+
+        OrderedVec(Vec::from(&self.0[..idx]))
+    }
+
     pub fn copy_split(&self, key: &K) -> (Self, Self)
     where
         K: Clone,