diff --git a/Cargo.lock b/Cargo.lock
index 832646e6..ae9e6dd1 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -383,6 +383,15 @@ version = "1.19.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3fdb12b2476b595f9358c5161aa467c2438859caa136dec86c26fdd2efe17b92"
 
+[[package]]
+name = "ordered-float"
+version = "5.3.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b7d950ca161dc355eaf28f82b11345ed76c6e1f6eb1f4f4479e0323b9e2fbd0e"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "pkg-config"
 version = "0.3.30"
@@ -600,6 +609,7 @@ dependencies = [
  "chrono",
  "clap",
  "libc",
+ "ordered-float",
  "pkg-config",
  "rand",
  "rand_distr",
diff --git a/Cargo.toml b/Cargo.toml
index 811c9043..b853fb9e 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -36,6 +36,7 @@ serde_json = {version = "1.0.120"}
 bincode = "1.3.1"
 rand = "0.8.6"
 rand_distr = "0.4.0"
+ordered-float = "5.3.0"
 
 [build-dependencies]
 bindgen = "0.69.4"
diff --git a/src/sys/treeseq.rs b/src/sys/treeseq.rs
index 0095d59f..499584a1 100644
--- a/src/sys/treeseq.rs
+++ b/src/sys/treeseq.rs
@@ -220,6 +220,22 @@ impl TreeSequence {
             current_row: 0,
         }
     }
+
+    pub fn breakpoints(&self) -> &[super::newtypes::Position] {
+        assert!(!self.as_ref().breakpoints.is_null());
+        let size = 1 + usize::try_from(self.num_trees()).unwrap();
+
+        // SAFETY: pointer is not NULL, the size is correct,
+        // and Position is a simple newtype for f64
+        unsafe {
+            std::slice::from_raw_parts(
+                self.as_ref()
+                    .breakpoints
+                    .cast::<super::newtypes::Position>(),
+                size,
+            )
+        }
+    }
 }
 
 #[test]
diff --git a/src/trees/treeseq.rs b/src/trees/treeseq.rs
index dcbbca49..47f7500a 100644
--- a/src/trees/treeseq.rs
+++ b/src/trees/treeseq.rs
@@ -769,6 +769,11 @@ impl TreeSequence {
     pub fn into_mut_ptr(self) -> Option<std::ptr::NonNull<tsk_treeseq_t>> {
         std::ptr::NonNull::new(self.inner.into_raw())
     }
+
+    /// Breakpoint positions, including 0.0 and the sequence length
+    pub fn breakpoints(&self) -> &[Position] {
+        self.inner.breakpoints()
+    }
 }
 
 impl TryFrom<TableCollection> for TreeSequence {
diff --git a/tests/test_trees.rs b/tests/test_trees.rs
index 4cfa03ff..bd049434 100644
--- a/tests/test_trees.rs
+++ b/tests/test_trees.rs
@@ -1190,3 +1190,26 @@ fn flatten_nodes_from_individuals() {
         .collect::<Vec<_>>();
     assert_eq!(nodes, &[0, 1, 2, 3, 4]);
 }
+
+#[test]
+fn test_breakpoints() {
+    let ts = treeseq_from_small_table_collection_two_trees();
+    let bp = ts.breakpoints();
+    assert_eq!(bp.len(), usize::try_from(ts.num_trees()).unwrap() + 1);
+    let mut tbp = vec![];
+    let mut tree_iterator = ts.tree_iterator(0).unwrap();
+    while let Some(tree) = tree_iterator.next() {
+        let l: f64 = tree.interval().0.into();
+        let r: f64 = tree.interval().1.into();
+        tbp.push(ordered_float::NotNan::new(l).unwrap());
+        tbp.push(ordered_float::NotNan::new(r).unwrap());
+    }
+    tbp.sort_unstable();
+    tbp.dedup();
+    assert_eq!(bp.len(), tbp.len());
+    for (i, j) in bp.iter().zip(tbp.iter()) {
+        let l = f64::from(i);
+        let r = f64::from(*j);
+        assert_eq!(l, r)
+    }
+}