diff --git a/library/core/src/cmp.rs b/library/core/src/cmp.rs
index 1d3466696ed04..ac286c171f080 100644
--- a/library/core/src/cmp.rs
+++ b/library/core/src/cmp.rs
@@ -22,6 +22,8 @@
 
 #![stable(feature = "rust1", since = "1.0.0")]
 
+use crate::marker::Destruct;
+
 use self::Ordering::*;
 
 /// Trait for equality comparisons which are [partial equivalence
@@ -603,7 +605,8 @@ impl Ordering {
 pub struct Reverse<T>(#[stable(feature = "reverse_cmp_key", since = "1.19.0")] pub T);
 
 #[stable(feature = "reverse_cmp_key", since = "1.19.0")]
-impl<T: PartialOrd> PartialOrd for Reverse<T> {
+#[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+impl<T: ~const PartialOrd> const PartialOrd for Reverse<T> {
     #[inline]
     fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
         other.0.partial_cmp(&self.0)
@@ -761,6 +764,7 @@ impl<T: Clone> Clone for Reverse<T> {
 #[doc(alias = ">=")]
 #[stable(feature = "rust1", since = "1.0.0")]
 #[rustc_diagnostic_item = "Ord"]
+#[const_trait]
 pub trait Ord: Eq + PartialOrd<Self> {
     /// This method returns an [`Ordering`] between `self` and `other`.
     ///
@@ -796,8 +800,15 @@ pub trait Ord: Eq + PartialOrd<Self> {
     fn max(self, other: Self) -> Self
     where
         Self: Sized,
+        Self: ~const Destruct,
     {
-        max_by(self, other, Ord::cmp)
+        // HACK(fee1-dead): go back to using `self.max_by(other, Ord::cmp)`
+        // when trait methods are allowed to be used when a const closure is
+        // expected.
+        match self.cmp(&other) {
+            Ordering::Less | Ordering::Equal => other,
+            Ordering::Greater => self,
+        }
     }
 
     /// Compares and returns the minimum of two values.
@@ -816,8 +827,15 @@ pub trait Ord: Eq + PartialOrd<Self> {
     fn min(self, other: Self) -> Self
     where
         Self: Sized,
+        Self: ~const Destruct,
     {
-        min_by(self, other, Ord::cmp)
+        // HACK(fee1-dead): go back to using `self.min_by(other, Ord::cmp)`
+        // when trait methods are allowed to be used when a const closure is
+        // expected.
+        match self.cmp(&other) {
+            Ordering::Less | Ordering::Equal => self,
+            Ordering::Greater => other,
+        }
     }
 
     /// Restrict a value to a certain interval.
@@ -841,6 +859,8 @@ pub trait Ord: Eq + PartialOrd<Self> {
     fn clamp(self, min: Self, max: Self) -> Self
     where
         Self: Sized,
+        Self: ~const Destruct,
+        Self: ~const PartialOrd,
     {
         assert!(min <= max);
         if self < min {
@@ -862,7 +882,8 @@ pub macro Ord($item:item) {
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
-impl Ord for Ordering {
+#[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+impl const Ord for Ordering {
     #[inline]
     fn cmp(&self, other: &Ordering) -> Ordering {
         (*self as i32).cmp(&(*other as i32))
@@ -870,7 +891,8 @@ impl Ord for Ordering {
 }
 
 #[stable(feature = "rust1", since = "1.0.0")]
-impl PartialOrd for Ordering {
+#[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+impl const PartialOrd for Ordering {
     #[inline]
     fn partial_cmp(&self, other: &Ordering) -> Option<Ordering> {
         (*self as i32).partial_cmp(&(*other as i32))
@@ -1187,8 +1209,9 @@ pub macro PartialOrd($item:item) {
 #[inline]
 #[must_use]
 #[stable(feature = "rust1", since = "1.0.0")]
+#[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
 #[cfg_attr(not(test), rustc_diagnostic_item = "cmp_min")]
-pub fn min<T: Ord>(v1: T, v2: T) -> T {
+pub const fn min<T: ~const Ord + ~const Destruct>(v1: T, v2: T) -> T {
     v1.min(v2)
 }
 
@@ -1250,8 +1273,9 @@ pub fn min_by_key<T, F: FnMut(&T) -> K, K: Ord>(v1: T, v2: T, mut f: F) -> T {
 #[inline]
 #[must_use]
 #[stable(feature = "rust1", since = "1.0.0")]
+#[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
 #[cfg_attr(not(test), rustc_diagnostic_item = "cmp_max")]
-pub fn max<T: Ord>(v1: T, v2: T) -> T {
+pub const fn max<T: ~const Ord + ~const Destruct>(v1: T, v2: T) -> T {
     v1.max(v2)
 }
 
@@ -1304,7 +1328,8 @@ mod impls {
     macro_rules! partial_eq_impl {
         ($($t:ty)*) => ($(
             #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialEq for $t {
+            #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+            impl const PartialEq for $t {
                 #[inline]
                 fn eq(&self, other: &$t) -> bool { (*self) == (*other) }
                 #[inline]
@@ -1314,7 +1339,8 @@ mod impls {
     }
 
     #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialEq for () {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const PartialEq for () {
         #[inline]
         fn eq(&self, _other: &()) -> bool {
             true
@@ -1341,7 +1367,8 @@ mod impls {
     macro_rules! partial_ord_impl {
         ($($t:ty)*) => ($(
             #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialOrd for $t {
+            #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+            impl const PartialOrd for $t {
                 #[inline]
                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
                     match (*self <= *other, *self >= *other) {
@@ -1364,7 +1391,8 @@ mod impls {
     }
 
     #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialOrd for () {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const PartialOrd for () {
         #[inline]
         fn partial_cmp(&self, _: &()) -> Option<Ordering> {
             Some(Equal)
@@ -1372,7 +1400,8 @@ mod impls {
     }
 
     #[stable(feature = "rust1", since = "1.0.0")]
-    impl PartialOrd for bool {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const PartialOrd for bool {
         #[inline]
         fn partial_cmp(&self, other: &bool) -> Option<Ordering> {
             Some(self.cmp(other))
@@ -1384,7 +1413,8 @@ mod impls {
     macro_rules! ord_impl {
         ($($t:ty)*) => ($(
             #[stable(feature = "rust1", since = "1.0.0")]
-            impl PartialOrd for $t {
+            #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+            impl const PartialOrd for $t {
                 #[inline]
                 fn partial_cmp(&self, other: &$t) -> Option<Ordering> {
                     Some(self.cmp(other))
@@ -1400,7 +1430,8 @@ mod impls {
             }
 
             #[stable(feature = "rust1", since = "1.0.0")]
-            impl Ord for $t {
+            #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+            impl const Ord for $t {
                 #[inline]
                 fn cmp(&self, other: &$t) -> Ordering {
                     // The order here is important to generate more optimal assembly.
@@ -1414,7 +1445,8 @@ mod impls {
     }
 
     #[stable(feature = "rust1", since = "1.0.0")]
-    impl Ord for () {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const Ord for () {
         #[inline]
         fn cmp(&self, _other: &()) -> Ordering {
             Equal
@@ -1422,7 +1454,8 @@ mod impls {
     }
 
     #[stable(feature = "rust1", since = "1.0.0")]
-    impl Ord for bool {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const Ord for bool {
         #[inline]
         fn cmp(&self, other: &bool) -> Ordering {
             // Casting to i8's and converting the difference to an Ordering generates
@@ -1441,7 +1474,8 @@ mod impls {
     ord_impl! { char usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128 }
 
     #[unstable(feature = "never_type", issue = "35121")]
-    impl PartialEq for ! {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const PartialEq for ! {
         fn eq(&self, _: &!) -> bool {
             *self
         }
@@ -1451,14 +1485,16 @@ mod impls {
     impl Eq for ! {}
 
     #[unstable(feature = "never_type", issue = "35121")]
-    impl PartialOrd for ! {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const PartialOrd for ! {
         fn partial_cmp(&self, _: &!) -> Option<Ordering> {
             *self
         }
     }
 
     #[unstable(feature = "never_type", issue = "35121")]
-    impl Ord for ! {
+    #[rustc_const_unstable(feature = "const_cmp", issue = "92391")]
+    impl const Ord for ! {
         fn cmp(&self, _: &!) -> Ordering {
             *self
         }
diff --git a/library/core/src/lib.rs b/library/core/src/lib.rs
index f24a7ab61ae89..30f2f0ee05c25 100644
--- a/library/core/src/lib.rs
+++ b/library/core/src/lib.rs
@@ -105,6 +105,7 @@
 #![feature(const_cell_into_inner)]
 #![feature(const_char_convert)]
 #![feature(const_clone)]
+#![feature(const_cmp)]
 #![feature(const_discriminant)]
 #![feature(const_eval_select)]
 #![feature(const_float_bits_conv)]