diff --git a/library/alloc/src/collections/btree/map.rs b/library/alloc/src/collections/btree/map.rs
index 4b649e43371dee25eaae95c3758662305ea22366..70a838a35f9d202b0af56357af0a4da9382d0536 100644
--- a/library/alloc/src/collections/btree/map.rs
+++ b/library/alloc/src/collections/btree/map.rs
@@ -233,9 +233,7 @@ fn clone_subtree<'a, K: Clone, V: Clone>(
         }
 
         if self.is_empty() {
-            // Ideally we'd call `BTreeMap::new` here, but that has the `K:
-            // Ord` constraint, which this method lacks.
-            BTreeMap { root: None, length: 0 }
+            BTreeMap::new()
         } else {
             clone_subtree(self.root.as_ref().unwrap().reborrow()) // unwrap succeeds because not empty
         }
@@ -499,10 +497,7 @@ impl<K, V> BTreeMap<K, V> {
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     #[rustc_const_unstable(feature = "const_btree_new", issue = "71835")]
-    pub const fn new() -> BTreeMap<K, V>
-    where
-        K: Ord,
-    {
+    pub const fn new() -> BTreeMap<K, V> {
         BTreeMap { root: None, length: 0 }
     }
 
@@ -522,7 +517,7 @@ pub const fn new() -> BTreeMap<K, V>
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     pub fn clear(&mut self) {
-        *self = BTreeMap { root: None, length: 0 };
+        *self = BTreeMap::new();
     }
 
     /// Returns a reference to the value corresponding to the key.
@@ -1957,7 +1952,7 @@ fn hash<H: Hasher>(&self, state: &mut H) {
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
-impl<K: Ord, V> Default for BTreeMap<K, V> {
+impl<K, V> Default for BTreeMap<K, V> {
     /// Creates an empty `BTreeMap`.
     fn default() -> BTreeMap<K, V> {
         BTreeMap::new()
diff --git a/library/alloc/src/collections/btree/map/tests.rs b/library/alloc/src/collections/btree/map/tests.rs
index 17e538483431ca0573317c64f98248920eeb7f7a..a99d6c49ab7b372b286d9d901985fe61129d5082 100644
--- a/library/alloc/src/collections/btree/map/tests.rs
+++ b/library/alloc/src/collections/btree/map/tests.rs
@@ -1745,7 +1745,7 @@ fn vacant_entry<T: Send + Ord + Default>(v: &mut BTreeMap<T, T>) -> impl Send +
     }
 }
 
-#[allow(dead_code)]
+#[test]
 fn test_ord_absence() {
     fn map<K>(mut map: BTreeMap<K, ()>) {
         map.is_empty();
@@ -1784,6 +1784,12 @@ fn map_debug<K: Debug>(mut map: BTreeMap<K, ()>) {
     fn map_clone<K: Clone>(mut map: BTreeMap<K, ()>) {
         map.clone_from(&map.clone());
     }
+
+    #[derive(Debug, Clone)]
+    struct NonOrd;
+    map(BTreeMap::<NonOrd, _>::new());
+    map_debug(BTreeMap::<NonOrd, _>::new());
+    map_clone(BTreeMap::<NonOrd, _>::default());
 }
 
 #[test]
diff --git a/library/alloc/src/collections/btree/set.rs b/library/alloc/src/collections/btree/set.rs
index 0c268ad32b2612b4d0cd070ca99e2fbf2807e050..ff0db22e0cc2d48519bbfac8ffb37f4752cce3a0 100644
--- a/library/alloc/src/collections/btree/set.rs
+++ b/library/alloc/src/collections/btree/set.rs
@@ -246,10 +246,7 @@ impl<T> BTreeSet<T> {
     /// ```
     #[stable(feature = "rust1", since = "1.0.0")]
     #[rustc_const_unstable(feature = "const_btree_new", issue = "71835")]
-    pub const fn new() -> BTreeSet<T>
-    where
-        T: Ord,
-    {
+    pub const fn new() -> BTreeSet<T> {
         BTreeSet { map: BTreeMap::new() }
     }
 
@@ -1192,7 +1189,7 @@ fn extend_one(&mut self, &elem: &'a T) {
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
-impl<T: Ord> Default for BTreeSet<T> {
+impl<T> Default for BTreeSet<T> {
     /// Creates an empty `BTreeSet`.
     fn default() -> BTreeSet<T> {
         BTreeSet::new()
diff --git a/library/alloc/src/collections/btree/set/tests.rs b/library/alloc/src/collections/btree/set/tests.rs
index 5d590a26281d2b993d38aea9e7e6e1ca0eba46eb..0a87ae12d61a59a34f957903aef3d0958010b9e6 100644
--- a/library/alloc/src/collections/btree/set/tests.rs
+++ b/library/alloc/src/collections/btree/set/tests.rs
@@ -607,7 +607,7 @@ fn union<T: Send + Sync + Ord>(v: &BTreeSet<T>) -> impl Send + '_ {
     }
 }
 
-#[allow(dead_code)]
+#[test]
 fn test_ord_absence() {
     fn set<K>(mut set: BTreeSet<K>) {
         set.is_empty();
@@ -626,6 +626,12 @@ fn set_debug<K: Debug>(set: BTreeSet<K>) {
     fn set_clone<K: Clone>(mut set: BTreeSet<K>) {
         set.clone_from(&set.clone());
     }
+
+    #[derive(Debug, Clone)]
+    struct NonOrd;
+    set(BTreeSet::<NonOrd>::new());
+    set_debug(BTreeSet::<NonOrd>::new());
+    set_clone(BTreeSet::<NonOrd>::default());
 }
 
 #[test]
diff --git a/library/alloc/tests/const_fns.rs b/library/alloc/tests/const_fns.rs
index da58ae92e112489516b49391f71bd1130f0b2f79..f448b3eb7c3000e611694fc018e0ca038faae4cb 100644
--- a/library/alloc/tests/const_fns.rs
+++ b/library/alloc/tests/const_fns.rs
@@ -1,29 +1,5 @@
 // Test const functions in the library
 
-use core::cmp::Ordering;
-
-// FIXME remove this struct once we put `K: ?const Ord` on BTreeMap::new.
-#[derive(PartialEq, Eq, PartialOrd)]
-pub struct MyType;
-
-impl const Ord for MyType {
-    fn cmp(&self, _: &Self) -> Ordering {
-        Ordering::Equal
-    }
-
-    fn max(self, _: Self) -> Self {
-        Self
-    }
-
-    fn min(self, _: Self) -> Self {
-        Self
-    }
-
-    fn clamp(self, _: Self, _: Self) -> Self {
-        Self
-    }
-}
-
 pub const MY_VEC: Vec<usize> = Vec::new();
 pub const MY_VEC2: Vec<usize> = Default::default();
 
@@ -32,13 +8,13 @@ fn clamp(self, _: Self, _: Self) -> Self {
 
 use std::collections::{BTreeMap, BTreeSet};
 
-pub const MY_BTREEMAP: BTreeMap<MyType, MyType> = BTreeMap::new();
-pub const MAP: &'static BTreeMap<MyType, MyType> = &MY_BTREEMAP;
+pub const MY_BTREEMAP: BTreeMap<usize, usize> = BTreeMap::new();
+pub const MAP: &'static BTreeMap<usize, usize> = &MY_BTREEMAP;
 pub const MAP_LEN: usize = MAP.len();
 pub const MAP_IS_EMPTY: bool = MAP.is_empty();
 
-pub const MY_BTREESET: BTreeSet<MyType> = BTreeSet::new();
-pub const SET: &'static BTreeSet<MyType> = &MY_BTREESET;
+pub const MY_BTREESET: BTreeSet<usize> = BTreeSet::new();
+pub const SET: &'static BTreeSet<usize> = &MY_BTREESET;
 pub const SET_LEN: usize = SET.len();
 pub const SET_IS_EMPTY: bool = SET.is_empty();