diff --git a/tests/unit/test_data.py b/tests/unit/test_data.py
index 78c1c6df4..349d3d442 100644
--- a/tests/unit/test_data.py
+++ b/tests/unit/test_data.py
@@ -15,6 +15,7 @@
 
 import copy
 
+import numpy as np
 import numpy.testing as npt
 import pytest
 import tensorflow as tf
@@ -68,6 +69,26 @@ def test_dataset_raises_for_different_leading_shapes(
         Dataset(query_points, observations)
 
 
+def test_dataset_does_not_raise_with_unspecified_leading_dimension() -> None:
+    query_points = tf.zeros((2, 2))
+    observations = tf.zeros((2, 1))
+
+    query_points_var = tf.Variable(
+        initial_value=np.zeros((0, 2)),
+        shape=(None, 2),
+        dtype=tf.float64,
+    )
+    observations_var = tf.Variable(
+        initial_value=np.zeros((0, 1)),
+        shape=(None, 1),
+        dtype=tf.float64,
+    )
+
+    Dataset(query_points=query_points_var, observations=observations)
+    Dataset(query_points=query_points, observations=observations_var)
+    Dataset(query_points=query_points_var, observations=observations_var)
+
+
 @pytest.mark.parametrize(
     "query_points_shape, observations_shape",
     [
diff --git a/trieste/data.py b/trieste/data.py
index 6c979a30e..5897efdff 100644
--- a/trieste/data.py
+++ b/trieste/data.py
@@ -53,6 +53,7 @@ def __post_init__(self) -> None:
             self.query_points.shape[:-1] != self.observations.shape[:-1]
             # can't check dynamic shapes, so trust that they're ok (if not, they'll fail later)
             and None not in self.query_points.shape[:-1]
+            and None not in self.observations.shape[:-1]
         ):
             raise ValueError(
                 f"Leading shapes of query_points and observations must match. Got shapes"