diff --git a/src/map.rs b/src/map.rs
index 872d4547..7fad92df 100644
--- a/src/map.rs
+++ b/src/map.rs
@@ -493,6 +493,48 @@ where
         }
     }
 
+    /// Insert a key-value pair in the map at its ordered position among keys
+    /// sorted by `cmp`.
+    ///
+    /// This is equivalent to finding the position with
+    /// [`binary_search_by`][Self::binary_search_by], then calling
+    /// [`insert_before`][Self::insert_before] for a new key.
+    ///
+    /// If the existing keys are **not** already sorted, then the insertion
+    /// index is unspecified (like [`slice::binary_search`]), but the key-value
+    /// pair is moved to or inserted at that position regardless.
+    ///
+    /// Computes in **O(n)** time (average).
+    pub fn insert_sorted_by<F>(&mut self, cmp: F, key: K, value: V) -> (usize, Option<V>)
+    where
+        K: Ord,
+        F: FnMut(&K, &V) -> Ordering,
+    {
+        let (Ok(i) | Err(i)) = self.binary_search_by(cmp);
+        self.insert_before(i, key, value)
+    }
+
+    /// Insert a key-value pair in the map at its ordered position among keys
+    /// sorted by `cmp`.
+    ///
+    /// This is equivalent to finding the position with
+    /// [`binary_search_by_key`][Self::binary_search_by_key] with `cmp(key)`, then
+    /// calling [`insert_before`][Self::insert_before] for a new key.
+    ///
+    /// If the existing keys are **not** already sorted, then the insertion
+    /// index is unspecified (like [`slice::binary_search`]), but the key-value
+    /// pair is moved to or inserted at that position regardless.
+    ///
+    /// Computes in **O(n)** time (average).
+    pub fn insert_sorted_by_key<F, B>(&mut self, mut cmp: F, key: K, value: V) -> (usize, Option<V>)
+    where
+        B: Ord,
+        F: FnMut(&K, &V) -> B,
+    {
+        let (Ok(i) | Err(i)) = self.binary_search_by_key(&cmp(&key, &value), cmp);
+        self.insert_before(i, key, value)
+    }
+
     /// Insert a key-value pair in the map before the entry at the given index, or at the end.
     ///
     /// If an equivalent key already exists in the map: the key remains and
diff --git a/src/map/tests.rs b/src/map/tests.rs
index 25ef7947..3d2470e4 100644
--- a/src/map/tests.rs
+++ b/src/map/tests.rs
@@ -1226,3 +1226,27 @@ fn disjoint_indices_mut_fail_duplicate() {
         Err(crate::GetDisjointMutError::OverlappingIndices)
     );
 }
+
+#[test]
+fn insert_sorted_by_key() {
+    let values = [(-1, 8), (3, 18), (-27, 2), (-2, 5)];
+    let mut map: IndexMap<i32, i32> = IndexMap::new();
+    for (key, value) in values.into_iter() {
+        map.insert_sorted_by_key(|k, _| k.abs(), key, value);
+    }
+    let values: Vec<_> = map.iter().map(|(k,v)|(*k,*v)).collect();
+    map.sort_by_cached_key(|key, _| key.abs());
+
+    assert_eq!(values, map.into_iter().collect::<Vec<_>>());
+}
+
+#[test]
+fn insert_sorted_by() {
+    let mut values = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)];
+    let mut map: IndexMap<i32, i32> = IndexMap::new();
+    for (key, value) in values.into_iter() {
+        map.insert_sorted_by(|probe, _| probe.cmp(&key).reverse(), key, value);
+    }
+    values.reverse();
+    assert_eq!(values, map.into_iter().collect::<Vec<_>>().as_slice());
+}
diff --git a/src/set.rs b/src/set.rs
index 3e54463e..e1b986c9 100644
--- a/src/set.rs
+++ b/src/set.rs
@@ -422,6 +422,56 @@ where
         (index, existing.is_none())
     }
 
+    /// Insert the value into the set at its ordered position among values
+    /// sorted by `cmp`.
+    ///
+    /// This is equivalent to finding the position with
+    /// [`binary_search_by`][Self::binary_search_by], then calling
+    /// [`insert_before`][Self::insert_before].
+    ///
+    /// If the sorted item is found in the set, it returns the index of that
+    /// existing item and `false`. Otherwise, it inserts the new item and
+    /// returns its sorted index and `true`.
+    ///
+    /// If the existing items are **not** already sorted, then the insertion
+    /// index is unspecified (like [`slice::binary_search`]), but the value
+    /// is moved to or inserted at that position regardless.
+    ///
+    /// Computes in **O(n)** time (average).
+    pub fn insert_sorted_by<F>(&mut self, mut cmp: F, value: T) -> (usize, bool)
+    where
+        T: Ord,
+        F: FnMut(&T) -> Ordering,
+    {
+        let (index, existing) = self.map.insert_sorted_by(|k, _| cmp(k), value, ());
+        (index, existing.is_none())
+    }
+
+    /// Insert the value into the set at its ordered position among values
+    /// sorted by `cmp`.
+    ///
+    /// This is equivalent to finding the position with
+    /// [`binary_search_by_key`][Self::binary_search_by] with `cmp(key)`, then
+    /// calling [`insert_before`][Self::insert_before].
+    ///
+    /// If the sorted item is found in the set, it returns the index of that
+    /// existing item and `false`. Otherwise, it inserts the new item and
+    /// returns its sorted index and `true`.
+    ///
+    /// If the existing items are **not** already sorted, then the insertion
+    /// index is unspecified (like [`slice::binary_search`]), but the value
+    /// is moved to or inserted at that position regardless.
+    ///
+    /// Computes in **O(n)** time (average).
+    pub fn insert_sorted_by_key<F, B>(&mut self, mut cmp: F, value: T) -> (usize, bool)
+    where
+        B: Ord,
+        F: FnMut(&T) -> B,
+    {
+        let (index, existing) = self.map.insert_sorted_by_key(|k, _| cmp(k), value, ());
+        (index, existing.is_none())
+    }
+
     /// Insert the value into the set before the value at the given index, or at the end.
     ///
     /// If an equivalent item already exists in the set, it returns `false` leaving the