diff --git a/src/arc.rs b/src/arc.rs
index 0abb26c..ecc5582 100644
--- a/src/arc.rs
+++ b/src/arc.rs
@@ -942,4 +942,90 @@ mod tests {
         assert_eq!([17, 19], *arc);
         assert_eq!(1, Arc::count(&arc));
     }
+
+    #[test]
+    fn arc_eq_and_cmp() {
+        [
+            [("*", &b"AB"[..]), ("*", &b"ab"[..])],
+            [("*", &b"AB"[..]), ("*", &b"a"[..])],
+            [("*", &b"A"[..]), ("*", &b"ab"[..])],
+            [("A", &b"*"[..]), ("a", &b"*"[..])],
+            [("a", &b"*"[..]), ("A", &b"*"[..])],
+            [("AB", &b"*"[..]), ("a", &b"*"[..])],
+            [("A", &b"*"[..]), ("ab", &b"*"[..])],
+        ]
+        .iter()
+        .for_each(|[lt @ (lh, ls), rt @ (rh, rs)]| {
+            let l = Arc::from_header_and_slice(lh, ls);
+            let r = Arc::from_header_and_slice(rh, rs);
+
+            assert_eq!(l, l);
+            assert_eq!(r, r);
+
+            assert_ne!(l, r);
+            assert_ne!(r, l);
+
+            assert_eq!(l <= l, lt <= lt, "{lt:?} <= {lt:?}");
+            assert_eq!(l >= l, lt >= lt, "{lt:?} >= {lt:?}");
+
+            assert_eq!(l < l, lt < lt, "{lt:?} < {lt:?}");
+            assert_eq!(l > l, lt > lt, "{lt:?} > {lt:?}");
+
+            assert_eq!(r <= r, rt <= rt, "{rt:?} <= {rt:?}");
+            assert_eq!(r >= r, rt >= rt, "{rt:?} >= {rt:?}");
+
+            assert_eq!(r < r, rt < rt, "{rt:?} < {rt:?}");
+            assert_eq!(r > r, rt > rt, "{rt:?} > {rt:?}");
+
+            assert_eq!(l < r, lt < rt, "{lt:?} < {rt:?}");
+            assert_eq!(r > l, rt > lt, "{rt:?} > {lt:?}");
+        })
+    }
+
+    #[test]
+    fn arc_eq_and_partial_cmp() {
+        [
+            [(0.0, &[0.0, 0.0][..]), (1.0, &[0.0, 0.0][..])],
+            [(1.0, &[0.0, 0.0][..]), (0.0, &[0.0, 0.0][..])],
+            [(0.0, &[0.0][..]), (0.0, &[0.0, 0.0][..])],
+            [(0.0, &[0.0, 0.0][..]), (0.0, &[0.0][..])],
+            [(0.0, &[1.0, 2.0][..]), (0.0, &[10.0, 20.0][..])],
+        ]
+        .iter()
+        .for_each(|[lt @ (lh, ls), rt @ (rh, rs)]| {
+            let l = Arc::from_header_and_slice(lh, ls);
+            let r = Arc::from_header_and_slice(rh, rs);
+
+            assert_eq!(l, l);
+            assert_eq!(r, r);
+
+            assert_ne!(l, r);
+            assert_ne!(r, l);
+
+            assert_eq!(l <= l, lt <= lt, "{lt:?} <= {lt:?}");
+            assert_eq!(l >= l, lt >= lt, "{lt:?} >= {lt:?}");
+
+            assert_eq!(l < l, lt < lt, "{lt:?} < {lt:?}");
+            assert_eq!(l > l, lt > lt, "{lt:?} > {lt:?}");
+
+            assert_eq!(r <= r, rt <= rt, "{rt:?} <= {rt:?}");
+            assert_eq!(r >= r, rt >= rt, "{rt:?} >= {rt:?}");
+
+            assert_eq!(r < r, rt < rt, "{rt:?} < {rt:?}");
+            assert_eq!(r > r, rt > rt, "{rt:?} > {rt:?}");
+
+            assert_eq!(l < r, lt < rt, "{lt:?} < {rt:?}");
+            assert_eq!(r > l, rt > lt, "{rt:?} > {lt:?}");
+        })
+    }
+
+    #[allow(dead_code)]
+    const fn is_partial_ord<T: ?Sized + PartialOrd>() {}
+
+    #[allow(dead_code)]
+    const fn is_ord<T: ?Sized + Ord>() {}
+
+    // compile-time check that PartialOrd/Ord is correctly derived
+    const _: () = is_partial_ord::<Arc<f64>>();
+    const _: () = is_ord::<Arc<u64>>();
 }
diff --git a/src/header.rs b/src/header.rs
index 6bc2d82..403f0ba 100644
--- a/src/header.rs
+++ b/src/header.rs
@@ -2,6 +2,7 @@ use alloc::alloc::Layout;
 use alloc::boxed::Box;
 use alloc::string::String;
 use alloc::vec::Vec;
+use core::cmp::Ordering;
 use core::iter::{ExactSizeIterator, Iterator};
 use core::marker::PhantomData;
 use core::mem::{self, ManuallyDrop};
@@ -12,7 +13,7 @@ use super::{Arc, ArcInner};
 
 /// Structure to allow Arc-managing some fixed-sized data and a variably-sized
 /// slice in a single allocation.
-#[derive(Debug, Eq, PartialEq, Hash, PartialOrd)]
+#[derive(Debug, Eq, PartialEq, Hash, PartialOrd, Ord)]
 #[repr(C)]
 pub struct HeaderSlice<H, T: ?Sized> {
     /// The fixed-sized data.
@@ -153,7 +154,7 @@ impl<H> Arc<HeaderSlice<H, str>> {
 
 /// Header data with an inline length. Consumers that use HeaderWithLength as the
 /// Header type in HeaderSlice can take advantage of ThinArc.
-#[derive(Debug, Eq, PartialEq, Hash, PartialOrd)]
+#[derive(Debug, Eq, PartialEq, Hash)]
 #[repr(C)]
 pub struct HeaderWithLength<H> {
     /// The fixed-sized data.
@@ -253,6 +254,18 @@ impl<T> From<Vec<T>> for Arc<[T]> {
 
 pub(crate) type HeaderSliceWithLength<H, T> = HeaderSlice<HeaderWithLength<H>, T>;
 
+impl<H: PartialOrd, T: ?Sized + PartialOrd> PartialOrd for HeaderSliceWithLength<H, T> {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        (&self.header.header, &self.slice).partial_cmp(&(&other.header.header, &other.slice))
+    }
+}
+
+impl<H: Ord, T: ?Sized + Ord> Ord for HeaderSliceWithLength<H, T> {
+    fn cmp(&self, other: &Self) -> Ordering {
+        (&self.header.header, &self.slice).cmp(&(&other.header.header, &other.slice))
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use alloc::boxed::Box;
diff --git a/src/thin_arc.rs b/src/thin_arc.rs
index e048468..19bb399 100644
--- a/src/thin_arc.rs
+++ b/src/thin_arc.rs
@@ -1,3 +1,4 @@
+use core::cmp::Ordering;
 use core::ffi::c_void;
 use core::fmt;
 use core::hash::{Hash, Hasher};
@@ -209,6 +210,20 @@ impl<H: PartialEq, T: PartialEq> PartialEq for ThinArc<H, T> {
 
 impl<H: Eq, T: Eq> Eq for ThinArc<H, T> {}
 
+impl<H: PartialOrd, T: PartialOrd> PartialOrd for ThinArc<H, T> {
+    #[inline]
+    fn partial_cmp(&self, other: &ThinArc<H, T>) -> Option<Ordering> {
+        ThinArc::with_arc(self, |a| ThinArc::with_arc(other, |b| a.partial_cmp(b)))
+    }
+}
+
+impl<H: Ord, T: Ord> Ord for ThinArc<H, T> {
+    #[inline]
+    fn cmp(&self, other: &ThinArc<H, T>) -> Ordering {
+        ThinArc::with_arc(self, |a| ThinArc::with_arc(other, |b| a.cmp(b)))
+    }
+}
+
 impl<H: Hash, T: Hash> Hash for ThinArc<H, T> {
     fn hash<HSR: Hasher>(&self, state: &mut HSR) {
         ThinArc::with_arc(self, |a| a.hash(state))
@@ -326,4 +341,92 @@ mod tests {
         }
         assert_eq!(canary.load(Acquire), 1);
     }
+
+    #[test]
+    fn thin_eq_and_cmp() {
+        [
+            [("*", &b"AB"[..]), ("*", &b"ab"[..])],
+            [("*", &b"AB"[..]), ("*", &b"a"[..])],
+            [("*", &b"A"[..]), ("*", &b"ab"[..])],
+            [("A", &b"*"[..]), ("a", &b"*"[..])],
+            [("a", &b"*"[..]), ("A", &b"*"[..])],
+            [("AB", &b"*"[..]), ("a", &b"*"[..])],
+            [("A", &b"*"[..]), ("ab", &b"*"[..])],
+        ]
+        .iter()
+        .for_each(|[lt @ (lh, ls), rt @ (rh, rs)]| {
+            let l = ThinArc::from_header_and_slice(lh, ls);
+            let r = ThinArc::from_header_and_slice(rh, rs);
+
+            assert_eq!(l, l);
+            assert_eq!(r, r);
+
+            assert_ne!(l, r);
+            assert_ne!(r, l);
+
+            assert_eq!(l <= l, lt <= lt, "{lt:?} <= {lt:?}");
+            assert_eq!(l >= l, lt >= lt, "{lt:?} >= {lt:?}");
+
+            assert_eq!(l < l, lt < lt, "{lt:?} < {lt:?}");
+            assert_eq!(l > l, lt > lt, "{lt:?} > {lt:?}");
+
+            assert_eq!(r <= r, rt <= rt, "{rt:?} <= {rt:?}");
+            assert_eq!(r >= r, rt >= rt, "{rt:?} >= {rt:?}");
+
+            assert_eq!(r < r, rt < rt, "{rt:?} < {rt:?}");
+            assert_eq!(r > r, rt > rt, "{rt:?} > {rt:?}");
+
+            assert_eq!(l < r, lt < rt, "{lt:?} < {rt:?}");
+            assert_eq!(r > l, rt > lt, "{rt:?} > {lt:?}");
+        })
+    }
+
+    #[test]
+    fn thin_eq_and_partial_cmp() {
+        [
+            [(0.0, &[0.0, 0.0][..]), (1.0, &[0.0, 0.0][..])],
+            [(1.0, &[0.0, 0.0][..]), (0.0, &[0.0, 0.0][..])],
+            [(0.0, &[0.0][..]), (0.0, &[0.0, 0.0][..])],
+            [(0.0, &[0.0, 0.0][..]), (0.0, &[0.0][..])],
+            [(0.0, &[1.0, 2.0][..]), (0.0, &[10.0, 20.0][..])],
+        ]
+        .iter()
+        .for_each(|[lt @ (lh, ls), rt @ (rh, rs)]| {
+            let l = ThinArc::from_header_and_slice(lh, ls);
+            let r = ThinArc::from_header_and_slice(rh, rs);
+
+            assert_eq!(l, l);
+            assert_eq!(r, r);
+
+            assert_ne!(l, r);
+            assert_ne!(r, l);
+
+            assert_eq!(l <= l, lt <= lt, "{lt:?} <= {lt:?}");
+            assert_eq!(l >= l, lt >= lt, "{lt:?} >= {lt:?}");
+
+            assert_eq!(l < l, lt < lt, "{lt:?} < {lt:?}");
+            assert_eq!(l > l, lt > lt, "{lt:?} > {lt:?}");
+
+            assert_eq!(r <= r, rt <= rt, "{rt:?} <= {rt:?}");
+            assert_eq!(r >= r, rt >= rt, "{rt:?} >= {rt:?}");
+
+            assert_eq!(r < r, rt < rt, "{rt:?} < {rt:?}");
+            assert_eq!(r > r, rt > rt, "{rt:?} > {rt:?}");
+
+            assert_eq!(l < r, lt < rt, "{lt:?} < {rt:?}");
+            assert_eq!(r > l, rt > lt, "{rt:?} > {lt:?}");
+        })
+    }
+
+    #[allow(dead_code)]
+    const fn is_partial_ord<T: ?Sized + PartialOrd>() {}
+
+    #[allow(dead_code)]
+    const fn is_ord<T: ?Sized + Ord>() {}
+
+    // compile-time check that PartialOrd/Ord is correctly derived
+    const _: () = is_partial_ord::<ThinArc<f64, f64>>();
+    const _: () = is_partial_ord::<ThinArc<f64, u64>>();
+    const _: () = is_partial_ord::<ThinArc<u64, f64>>();
+    const _: () = is_ord::<ThinArc<u64, u64>>();
 }