diff --git a/src/header/map.rs b/src/header/map.rs
index a123606e..de8bd2d2 100644
--- a/src/header/map.rs
+++ b/src/header/map.rs
@@ -2133,12 +2133,16 @@ impl<T> Extend<(Option<HeaderName>, T)> for HeaderMap<T> {
         // Reserve the entire hint lower bound if the map is empty.
         // Otherwise reserve half the hint (rounded up), so the map
         // will only resize twice in the worst case.
-        let reserve = if self.is_empty() {
+        let hint = if self.is_empty() {
             iter.size_hint().0
         } else {
             (iter.size_hint().0 + 1) / 2
         };
 
+        // Clamp the hint so an over-estimate cannot overflow `reserve`.
+        let max_reserve = usable_capacity(MAX_SIZE).saturating_sub(self.entries.len());
+        let reserve = hint.min(max_reserve);
+
         self.reserve(reserve);
 
         // The structure of this is a bit weird, but it is mostly to make the
@@ -2189,12 +2193,16 @@ impl<T> Extend<(HeaderName, T)> for HeaderMap<T> {
         // will only resize twice in the worst case.
         let iter = iter.into_iter();
 
-        let reserve = if self.is_empty() {
+        let hint = if self.is_empty() {
             iter.size_hint().0
         } else {
             (iter.size_hint().0 + 1) / 2
         };
 
+        // Clamp the hint so an over-estimate cannot overflow `reserve`.
+        let max_reserve = usable_capacity(MAX_SIZE).saturating_sub(self.entries.len());
+        let reserve = hint.min(max_reserve);
+
         self.reserve(reserve);
 
         for (k, v) in iter {
diff --git a/tests/header_map.rs b/tests/header_map.rs
index 9a9d7e12..8f407fd9 100644
--- a/tests/header_map.rs
+++ b/tests/header_map.rs
@@ -55,6 +55,23 @@ fn with_capacity_overflow() {
     HeaderMap::<u32>::with_capacity(24_577);
 }
 
+#[test]
+fn extend_size_hint_above_capacity() {
+    // A `HeaderMap` may hold more values than the table can index when many
+    // values are appended under one name, so an exact size hint can exceed the
+    // largest `reserve` request. Extending must not panic in that case.
+    let name = HeaderName::from_static("h");
+    let value = HeaderValue::from_static("0");
+    let pairs: Vec<(HeaderName, HeaderValue)> =
+        std::iter::repeat_with(|| (name.clone(), value.clone()))
+            .take(24_577)
+            .collect();
+
+    let map = HeaderMap::from_iter(pairs);
+    assert_eq!(map.len(), 24_577);
+    assert_eq!(map.keys_len(), 1);
+}
+
 #[test]
 #[should_panic]
 fn reserve_overflow() {