diff --git a/metomi/isodatetime/tests/test_01.py b/metomi/isodatetime/tests/test_01.py
index 0fcc5a4..d870967 100644
--- a/metomi/isodatetime/tests/test_01.py
+++ b/metomi/isodatetime/tests/test_01.py
@@ -703,14 +703,25 @@ def test_timepoint_plus_float_time_duration_day_of_month_type():
     assert isinstance(time_point.day_of_month, int)
 
 
-def test_timepoint_subtract():
+@pytest.mark.parametrize(
+    'test_props1, test_props2, ctrl_string', get_timepoint_subtract_tests()
+)
+def test_timepoint_subtract(test_props1, test_props2, ctrl_string):
     """Test subtracting one time point from another."""
-    for test_props1, test_props2, ctrl_string in (
-            get_timepoint_subtract_tests()):
-        point1 = data.TimePoint(**test_props1)
-        point2 = data.TimePoint(**test_props2)
-        test_string = str(point1 - point2)
-        assert test_string == ctrl_string
+    point1 = TimePoint(**test_props1)
+    point2 = TimePoint(**test_props2)
+    test_string = str(point1 - point2)
+    assert test_string == ctrl_string
+
+
+def test_timepoint_subtract_truncated():
+    """Test an error is raised if subtracting a truncated TimePoint from
+    a non-truncated one and vice versa."""
+    msg = r"Invalid subtraction"
+    with pytest.raises(ValueError, match=msg):
+        TimePoint(year=2000) - TimePoint(day_of_month=2, truncated=True)
+    with pytest.raises(ValueError, match=msg):
+        TimePoint(day_of_month=2, truncated=True) - TimePoint(year=2000)
 
 
 @pytest.mark.parametrize('test', get_duration_subtract_tests())
@@ -875,6 +886,11 @@ def test_timepoint_duration_subtract(test):
             ),
             data.TimePoint(year=3200, month_of_year=2, day_of_month=29),
         ),
+        add_param(
+            data.TimePoint(year=3012, month_of_year=10, hour_of_day=9),
+            data.TimePoint(day_of_year=63, truncated=True),
+            data.TimePoint(year=3013, day_of_year=63),
+        ),
     ],
 )
 def test_timepoint_add(