diff --git a/c/CHANGELOG.rst b/c/CHANGELOG.rst
index c1643e1ff1..c8dcb7143f 100644
--- a/c/CHANGELOG.rst
+++ b/c/CHANGELOG.rst
@@ -2,6 +2,11 @@
 [1.1.2] - 2023-XX-XX
 --------------------
 
+**Performance improvements**
+
+- tsk_tree_seek is now much faster at seeking to arbitrary points along
+  the sequence from the null tree (:user:`molpopgen`, :pr:`2661`).
+
 **Features**
 
 - The struct ``tsk_treeseq_t`` now has the variables ``min_time`` and ``max_time``,
@@ -24,6 +29,8 @@
 - Add `x_table_keep_rows` methods to provide efficient in-place table subsetting
   (:user:`jeromekelleher`, :pr:`2700`).
 
+- Add `tsk_tree_seek_index` function
+
 --------------------
 [1.1.1] - 2022-07-29
 --------------------
diff --git a/c/tests/test_trees.c b/c/tests/test_trees.c
index f0ced8585f..94e33ee487 100644
--- a/c/tests/test_trees.c
+++ b/c/tests/test_trees.c
@@ -6140,10 +6140,16 @@ test_seek_multi_tree(void)
         ret = tsk_tree_seek(&t, breakpoints[j], 0);
         CU_ASSERT_EQUAL_FATAL(ret, 0);
         CU_ASSERT_EQUAL_FATAL(t.index, j);
+        ret = tsk_tree_seek_index(&t, j, 0);
+        CU_ASSERT_EQUAL_FATAL(ret, 0);
+        CU_ASSERT_EQUAL_FATAL(t.index, j);
         for (k = 0; k < num_trees; k++) {
             ret = tsk_tree_seek(&t, breakpoints[k], 0);
             CU_ASSERT_EQUAL_FATAL(ret, 0);
             CU_ASSERT_EQUAL_FATAL(t.index, k);
+            ret = tsk_tree_seek_index(&t, k, 0);
+            CU_ASSERT_EQUAL_FATAL(ret, 0);
+            CU_ASSERT_EQUAL_FATAL(t.index, k);
         }
     }
 
@@ -6205,6 +6211,10 @@ test_seek_errors(void)
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_SEEK_OUT_OF_BOUNDS);
     ret = tsk_tree_seek(&t, 11, 0);
     CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_SEEK_OUT_OF_BOUNDS);
+    ret = tsk_tree_seek_index(&t, (tsk_id_t) ts.num_trees, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_SEEK_OUT_OF_BOUNDS);
+    ret = tsk_tree_seek_index(&t, -1, 0);
+    CU_ASSERT_EQUAL_FATAL(ret, TSK_ERR_SEEK_OUT_OF_BOUNDS);
 
     tsk_tree_free(&t);
     tsk_treeseq_free(&ts);
diff --git a/c/tskit/trees.c b/c/tskit/trees.c
index 06cad0e823..4604579e0b 100644
--- a/c/tskit/trees.c
+++ b/c/tskit/trees.c
@@ -4549,19 +4549,138 @@ tsk_tree_position_in_interval(const tsk_tree_t *self, double x)
     return self->interval.left <= x && x < self->interval.right;
 }
 
-int TSK_WARN_UNUSED
-tsk_tree_seek(tsk_tree_t *self, double x, tsk_flags_t TSK_UNUSED(options))
+/* NOTE:
+ *
+ * Notes from Kevin Thornton:
+ *
+ * This method inserts the edges for an arbitrary tree
+ * in linear time and requires no additional memory.
+ *
+ * During design, the following alternatives were tested
+ * (in a combination of rust + C):
+ * 1. Indexing edge insertion/removal locations by tree.
+ *    The indexing can be done in O(n) time, giving O(1)
+ *    access to the first edge in a tree. We can then add
+ *    edges to the tree in O(e) time, where e is the number
+ *    of edges. This apparoach requires O(n) additional memory
+ *    and is only marginally faster than the implementation below.
+ * 2. Building an interval tree mapping edge id -> span.
+ *    This approach adds a lot of complexity and wasn't any faster
+ *    than the indexing described above.
+ */
+static int
+tsk_tree_seek_from_null(tsk_tree_t *self, double x, tsk_flags_t TSK_UNUSED(options))
 {
     int ret = 0;
+    tsk_size_t edge;
+    tsk_id_t p, c, e, j, k, tree_index;
     const double L = tsk_treeseq_get_sequence_length(self->tree_sequence);
-    const double t_l = self->interval.left;
-    const double t_r = self->interval.right;
-    double distance_left, distance_right;
+    const tsk_treeseq_t *treeseq = self->tree_sequence;
+    const tsk_table_collection_t *tables = treeseq->tables;
+    const tsk_id_t *restrict edge_parent = tables->edges.parent;
+    const tsk_id_t *restrict edge_child = tables->edges.child;
+    const tsk_size_t num_edges = tables->edges.num_rows;
+    const tsk_size_t num_trees = self->tree_sequence->num_trees;
+    const double *restrict edge_left = tables->edges.left;
+    const double *restrict edge_right = tables->edges.right;
+    const double *restrict breakpoints = treeseq->breakpoints;
+    const tsk_id_t *restrict insertion = tables->indexes.edge_insertion_order;
+    const tsk_id_t *restrict removal = tables->indexes.edge_removal_order;
+
+    // NOTE: it may be better to get the
+    // index first and then ask if we are
+    // searching in the first or last 1/2
+    // of trees.
+    j = -1;
+    if (x <= L / 2.0) {
+        for (edge = 0; edge < num_edges; edge++) {
+            e = insertion[edge];
+            if (edge_left[e] > x) {
+                j = (tsk_id_t) edge;
+                break;
+            }
+            if (x >= edge_left[e] && x < edge_right[e]) {
+                p = edge_parent[e];
+                c = edge_child[e];
+                tsk_tree_insert_edge(self, p, c, e);
+            }
+        }
+    } else {
+        for (edge = 0; edge < num_edges; edge++) {
+            e = removal[num_edges - edge - 1];
+            if (edge_right[e] < x) {
+                j = (tsk_id_t)(num_edges - edge - 1);
+                while (j < (tsk_id_t) num_edges && edge_left[insertion[j]] <= x) {
+                    j++;
+                }
+                break;
+            }
+            if (x >= edge_left[e] && x < edge_right[e]) {
+                p = edge_parent[e];
+                c = edge_child[e];
+                tsk_tree_insert_edge(self, p, c, e);
+            }
+        }
+    }
 
-    if (x < 0 || x >= L) {
+    if (j == -1) {
+        j = 0;
+        while (j < (tsk_id_t) num_edges && edge_left[insertion[j]] <= x) {
+            j++;
+        }
+    }
+    k = 0;
+    while (k < (tsk_id_t) num_edges && edge_right[removal[k]] <= x) {
+        k++;
+    }
+
+    /* NOTE: tsk_search_sorted finds the first the first
+     * insertion locatiom >= the query point, which
+     * finds a RIGHT value for queries not at the left edge.
+     */
+    tree_index = (tsk_id_t) tsk_search_sorted(breakpoints, num_trees + 1, x);
+    if (breakpoints[tree_index] > x) {
+        tree_index--;
+    }
+    self->index = tree_index;
+    self->interval.left = breakpoints[tree_index];
+    self->interval.right = breakpoints[tree_index + 1];
+    self->left_index = j;
+    self->right_index = k;
+    self->direction = TSK_DIR_FORWARD;
+    self->num_nodes = tables->nodes.num_rows;
+    if (tables->sites.num_rows > 0) {
+        self->sites = treeseq->tree_sites[self->index];
+        self->sites_length = treeseq->tree_sites_length[self->index];
+    }
+
+    return ret;
+}
+
+int TSK_WARN_UNUSED
+tsk_tree_seek_index(tsk_tree_t *self, tsk_id_t tree, tsk_flags_t options)
+{
+    int ret = 0;
+    double x;
+
+    if (tree < 0 || tree >= (tsk_id_t) self->tree_sequence->num_trees) {
         ret = TSK_ERR_SEEK_OUT_OF_BOUNDS;
         goto out;
     }
+    x = self->tree_sequence->breakpoints[tree];
+    ret = tsk_tree_seek(self, x, options);
+out:
+    return ret;
+}
+
+static int TSK_WARN_UNUSED
+tsk_tree_seek_linear(tsk_tree_t *self, double x, tsk_flags_t TSK_UNUSED(options))
+{
+    const double L = tsk_treeseq_get_sequence_length(self->tree_sequence);
+    const double t_l = self->interval.left;
+    const double t_r = self->interval.right;
+    int ret = 0;
+    double distance_left, distance_right;
 
     if (x < t_l) {
         /* |-----|-----|========|---------| */
@@ -4594,6 +4713,27 @@ tsk_tree_seek(tsk_tree_t *self, double x, tsk_flags_t TSK_UNUSED(options))
     return ret;
 }
 
+int TSK_WARN_UNUSED
+tsk_tree_seek(tsk_tree_t *self, double x, tsk_flags_t options)
+{
+    int ret = 0;
+    const double L = tsk_treeseq_get_sequence_length(self->tree_sequence);
+
+    if (x < 0 || x >= L) {
+        ret = TSK_ERR_SEEK_OUT_OF_BOUNDS;
+        goto out;
+    }
+
+    if (self->index == -1) {
+        ret = tsk_tree_seek_from_null(self, x, options);
+    } else {
+        ret = tsk_tree_seek_linear(self, x, options);
+    }
+
+out:
+    return ret;
+}
+
 int TSK_WARN_UNUSED
 tsk_tree_clear(tsk_tree_t *self)
 {
diff --git a/c/tskit/trees.h b/c/tskit/trees.h
index 4a84bf3446..efe9980077 100644
--- a/c/tskit/trees.h
+++ b/c/tskit/trees.h
@@ -1192,12 +1192,6 @@ we will have ``position < tree.interval.right``.
 
 Seeking to a position currently covered by the tree is
 a constant time operation.
-
-.. warning::
-   The current implementation of ``seek`` does **not** provide efficient
-   random access to arbitrary positions along the genome. However,
-   sequentially seeking in either direction is as efficient as calling
-   :c:func:`tsk_tree_next` or :c:func:`tsk_tree_prev` directly.
 @endrst
 
 @param self A pointer to an initialised tsk_tree_t object.
@@ -1208,6 +1202,22 @@ a constant time operation.
 */
 int tsk_tree_seek(tsk_tree_t *self, double position, tsk_flags_t options);
 
+/**
+@brief Seek to a specific tree in a tree sequence.
+
+@rst
+Set the state of this tree to reflect the tree in parent
+tree sequence whose index is ``0 <= tree < num_trees``.
+@endrst
+
+@param self A pointer to an initialised tsk_tree_t object.
+@param tree The target tree index.
+@param options Seek options. Currently unused. Set to 0 for compatibility
+    with future versions of tskit.
+@return Return 0 on success or a negative value on failure.
+*/
+int tsk_tree_seek_index(tsk_tree_t *self, tsk_id_t tree, tsk_flags_t options);
+
 /** @} */
 
 /**
diff --git a/python/CHANGELOG.rst b/python/CHANGELOG.rst
index 3a81b2aa1c..4450bf06c4 100644
--- a/python/CHANGELOG.rst
+++ b/python/CHANGELOG.rst
@@ -2,6 +2,11 @@
 [0.5.5] - 2023-01-XX
 --------------------
 
+**Performance improvements**
+
+- Methods like ts.at() which seek to a specified position on the sequence from
+  a new Tree instance are now much faster (:user:`molpopgen`, :pr:`2661`).
+
 **Features**
 
 - Add ``__repr__`` for variants to return a string representation of the raw data
diff --git a/python/_tskitmodule.c b/python/_tskitmodule.c
index 2b379ff2b1..30c3e7743b 100644
--- a/python/_tskitmodule.c
+++ b/python/_tskitmodule.c
@@ -10658,6 +10658,29 @@ Tree_seek(Tree *self, PyObject *args)
     return ret;
 }
 
+static PyObject *
+Tree_seek_index(Tree *self, PyObject *args)
+{
+    PyObject *ret = NULL;
+    tsk_id_t index = 0;
+    int err;
+
+    if (Tree_check_state(self) != 0) {
+        goto out;
+    }
+    if (!PyArg_ParseTuple(args, "O&", tsk_id_converter, &index)) {
+        goto out;
+    }
+    err = tsk_tree_seek_index(self->tree, index, 0);
+    if (err != 0) {
+        handle_library_error(err);
+        goto out;
+    }
+    ret = Py_BuildValue("");
+out:
+    return ret;
+}
+
 static PyObject *
 Tree_clear(Tree *self)
 {
@@ -11796,6 +11819,10 @@ static PyMethodDef Tree_methods[] = {
         .ml_meth = (PyCFunction) Tree_seek,
         .ml_flags = METH_VARARGS,
         .ml_doc = "Seeks to the tree at the specified position" },
+    { .ml_name = "seek_index",
+        .ml_meth = (PyCFunction) Tree_seek_index,
+        .ml_flags = METH_VARARGS,
+        .ml_doc = "Seeks to the tree at the specified index" },
     { .ml_name = "clear",
         .ml_meth = (PyCFunction) Tree_clear,
         .ml_flags = METH_NOARGS,
diff --git a/python/tests/test_highlevel.py b/python/tests/test_highlevel.py
index c926121aea..ca67e24ce0 100644
--- a/python/tests/test_highlevel.py
+++ b/python/tests/test_highlevel.py
@@ -4598,10 +4598,13 @@ def test_index_from_different_directions(self, index):
             t2.prev()
         assert_same_tree_different_order(t1, t2)
 
-    def test_seek_0_from_null(self):
+    @pytest.mark.parametrize("position", [0, 1, 2, 3])
+    def test_seek_from_null(self, position):
         t1, t2 = self.setup()
-        t1.first()
-        t2.seek(0)
+        t1.clear()
+        t1.seek(position)
+        t2.first()
+        t2.seek(position)
         assert_trees_identical(t1, t2)
 
     @pytest.mark.parametrize("index", range(3))
@@ -4654,6 +4657,14 @@ def test_seek_3_from_null(self):
         t2.seek(3)
         assert_trees_identical(t1, t2)
 
+    def test_seek_3_from_null_prev(self):
+        t1, t2 = self.setup()
+        t1.last()
+        t1.prev()
+        t2.seek(3)
+        t2.prev()
+        assert_trees_identical(t1, t2)
+
     def test_seek_3_from_0(self):
         t1, t2 = self.setup()
         t1.last()
@@ -4669,6 +4680,37 @@ def test_seek_0_from_3(self):
         t2.seek(0)
         assert_trees_identical(t1, t2)
 
+    @pytest.mark.parametrize("ts", get_example_tree_sequences())
+    def test_seek_mid_null_and_middle(self, ts):
+        breakpoints = ts.breakpoints(as_array=True)
+        mid = breakpoints[:-1] + np.diff(breakpoints) / 2
+        for index, x in enumerate(mid[:-1]):
+            t1 = tskit.Tree(ts)
+            t1.seek(x)
+            # Also seek to this point manually to make sure we're not
+            # reusing the seek from null under the hood.
+            t2 = tskit.Tree(ts)
+            if index <= ts.num_trees / 2:
+                while t2.index != index:
+                    t2.next()
+            else:
+                while t2.index != index:
+                    t2.prev()
+            assert t1.index == t2.index
+            assert np.all(t1.parent_array == t2.parent_array)
+
+    @pytest.mark.parametrize("ts", get_example_tree_sequences())
+    def test_seek_last_then_prev(self, ts):
+        t1 = tskit.Tree(ts)
+        t1.seek(ts.sequence_length - 0.00001)
+        assert t1.index == ts.num_trees - 1
+        t2 = tskit.Tree(ts)
+        t2.prev()
+        assert_trees_identical(t1, t2)
+        t1.prev()
+        t2.prev()
+        assert_trees_identical(t1, t2)
+
 
 class TestSeek:
     @pytest.mark.parametrize("ts", get_example_tree_sequences())
diff --git a/python/tests/test_lowlevel.py b/python/tests/test_lowlevel.py
index 8bbc201b85..7ebe6467eb 100644
--- a/python/tests/test_lowlevel.py
+++ b/python/tests/test_lowlevel.py
@@ -2968,6 +2968,16 @@ def test_seek_errors(self):
             with pytest.raises(_tskit.LibraryError):
                 tree.seek(bad_pos)
 
+    def test_seek_index_errors(self):
+        ts = self.get_example_tree_sequence()
+        tree = _tskit.Tree(ts)
+        for bad_type in ["", "x", {}]:
+            with pytest.raises(TypeError):
+                tree.seek_index(bad_type)
+        for bad_index in [-1, 10**6]:
+            with pytest.raises(_tskit.LibraryError):
+                tree.seek_index(bad_index)
+
     def test_root_threshold(self):
         for ts in self.get_example_tree_sequences():
             tree = _tskit.Tree(ts)
diff --git a/python/tskit/trees.py b/python/tskit/trees.py
index 39a1e4c41a..da5a7f9d07 100644
--- a/python/tskit/trees.py
+++ b/python/tskit/trees.py
@@ -820,7 +820,6 @@ def seek_index(self, index):
 
         .. include:: substitutions/linear_traversal_warning.rst
 
-
         :param int index: The tree index to seek to.
         :raises IndexError: If an index outside the acceptable range is provided.
         """
@@ -829,12 +828,7 @@ def seek_index(self, index):
             index += num_trees
         if index < 0 or index >= num_trees:
             raise IndexError("Index out of bounds")
-        # This should be implemented in C efficiently using the indexes.
-        # No point in complicating the current implementation by trying
-        # to seek from the correct direction.
-        self.first()
-        while self.index != index:
-            self.next()
+        self._ll_tree.seek_index(index)
 
     def seek(self, position):
         """