diff --git a/Cargo.toml b/Cargo.toml
index 591a6e3..c0c6045 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -23,7 +23,7 @@ neon = []
 # --no-default-features, the only way to use the SIMD implementations in this
 # crate is to enable the corresponding instruction sets statically for the
 # entire build, with e.g. RUSTFLAGS="-C target-cpu=native".
-std = []
+std = ["subtle/std"]
 
 # The `rayon` feature (disabled by default, but enabled for docs.rs) adds the
 # `update_rayon` and (in combination with `mmap` below) `update_mmap_rayon`
@@ -94,12 +94,12 @@ features = ["mmap", "rayon", "serde", "zeroize"]
 [dependencies]
 arrayref = "0.3.5"
 arrayvec = { version = "0.7.4", default-features = false }
-constant_time_eq = "0.3.0"
 cfg-if = "1.0.0"
 digest = { version = "0.10.1", features = [ "mac" ], optional = true }
 memmap2 = { version = "0.9", optional = true }
 rayon = { version = "1.2.1", optional = true }
 serde = { version = "1.0", default-features = false, features = ["derive"], optional = true }
+subtle = { version = "2.5.0", default-features = false, features = ["i128"] }
 zeroize = { version = "1", default-features = false, features = ["zeroize_derive"], optional = true }
 
 [dev-dependencies]
diff --git a/src/lib.rs b/src/lib.rs
index 1fe47bf..fbbaabc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -135,9 +135,10 @@ mod join;
 
 use arrayref::{array_mut_ref, array_ref};
 use arrayvec::{ArrayString, ArrayVec};
-use core::cmp;
 use core::fmt;
+use core::{cmp, cmp::Ordering};
 use platform::{Platform, MAX_SIMD_DEGREE, MAX_SIMD_DEGREE_OR_2};
+use subtle::{ConditionallySelectable, ConstantTimeEq, ConstantTimeGreater};
 
 /// The number of bytes in a [`Hash`](struct.Hash.html), 32.
 pub const OUT_LEN: usize = 32;
@@ -309,7 +310,7 @@ impl core::str::FromStr for Hash {
 impl PartialEq for Hash {
     #[inline]
     fn eq(&self, other: &Hash) -> bool {
-        constant_time_eq::constant_time_eq_32(&self.0, &other.0)
+        self.0.ct_eq(&other.0).into()
     }
 }
 
@@ -317,7 +318,7 @@ impl PartialEq for Hash {
 impl PartialEq<[u8; OUT_LEN]> for Hash {
     #[inline]
     fn eq(&self, other: &[u8; OUT_LEN]) -> bool {
-        constant_time_eq::constant_time_eq_32(&self.0, other)
+        self.0.ct_eq(other).into()
     }
 }
 
@@ -325,12 +326,34 @@ impl PartialEq<[u8; OUT_LEN]> for Hash {
 impl PartialEq<[u8]> for Hash {
     #[inline]
     fn eq(&self, other: &[u8]) -> bool {
-        constant_time_eq::constant_time_eq(&self.0, other)
+        self.0.ct_eq(other).into()
     }
 }
 
 impl Eq for Hash {}
 
+/// This implementation is constant-time.
+impl PartialOrd for Hash {
+    #[inline]
+    fn partial_cmp(&self, other: &Hash) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for Hash {
+    #[inline]
+    fn cmp(&self, other: &Hash) -> Ordering {
+        let l0 = u128::from_le_bytes(self.0[..16].try_into().unwrap());
+        let h0 = u128::from_le_bytes(self.0[16..].try_into().unwrap());
+        let l1 = u128::from_le_bytes(other.0[..16].try_into().unwrap());
+        let h1 = u128::from_le_bytes(other.0[16..].try_into().unwrap());
+        let h0_gt_h1 = h0.ct_gt(&h1);
+        let l0_gt_l1 = l0.ct_gt(&l1);
+        // Return `Less` if `h0 < h1` and `l0 < l1`, otherwise, return `Greater`.
+        Ordering::conditional_select(&Ordering::Greater, &Ordering::Less, !h0_gt_h1 & !l0_gt_l1)
+    }
+}
+
 impl fmt::Display for Hash {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         // Formatting field as `&str` to reduce code size since the `Debug`