diff --git a/.github/workflows/ci-tests.yml b/.github/workflows/ci-tests.yml
index afdaa2b..5fec7cf 100644
--- a/.github/workflows/ci-tests.yml
+++ b/.github/workflows/ci-tests.yml
@@ -35,7 +35,7 @@ jobs:
 
       - name: "Install dependencies"
         run: |
-          conda install --yes pytest iris xarray filelock requests
+          conda install --yes "numpy<2" pytest iris xarray filelock requests
 
       - name: "Install *latest* Iris"
         run: |
diff --git a/requirements/readthedocs.yml b/requirements/readthedocs.yml
index 97930e5..4cce034 100644
--- a/requirements/readthedocs.yml
+++ b/requirements/readthedocs.yml
@@ -5,6 +5,7 @@ channels:
 
 dependencies:
   - netCDF4>=1.4
+  - numpy <2.0
   - iris
   - xarray
   - filelock
diff --git a/tests/data_testcase_schemas.py b/tests/data_testcase_schemas.py
index 26f8c7e..8ccb8af 100644
--- a/tests/data_testcase_schemas.py
+++ b/tests/data_testcase_schemas.py
@@ -43,12 +43,18 @@ def data_types():
     yield "string"
 
 
-# Just confirm that the above list of types matches those used by netCDF4, except for
-# 'string' replacing 'S1'.
-assert set(data_types()) == (
-    set(nc.default_fillvals.keys()) - set(["S1"]) | set(["string"])
+# Confirm that the above list of types matches those of netCDF4, with specific fixes
+# Get the dtype list from the netCDF default fill-values.
+_nc_dtypes = set(nc.default_fillvals.keys())
+# Remove the numpy-only complex types
+_nc_dtypes = set(
+    typename for typename in _nc_dtypes if np.dtype(typename).kind != "c"
 )
-
+# Also replace 'S1' with our own 'string' type marker
+_nc_dtypes.remove("S1")
+_nc_dtypes.add("string")
+# This should match the list of dtypes which we support (and test against)
+assert set(data_types()) == _nc_dtypes
 
 # Suitable test values for each attribute/data type.
 _INT_Approx_2x31 = int(2**31 - 1)
@@ -509,7 +515,17 @@ def standard_testcase(request, session_testdir):
     },
     "xarray": {
         # We think Xarray can load ~anything (maybe returning nothing)
-        "load": [],
+        "load": [
+            # .. except a few specific bounds variables generate a peculiar error
+            # """
+            #   xarray.core.variable.MissingDimensionsError: 'time_bnd' has more than
+            #   1-dimension and the same name as one of its dimensions
+            #   ('time', 'time_bnd'). xarray disallows such variables because they
+            #   conflict with the coordinates used to label dimensions.
+            # """
+            "small_rotPole_precipitation",
+            "small_FC_167",
+        ],
         # Xarray can save ~anything
         "save": [r"test_monotonic_coordinate"],
     },