diff --git a/Changelog.rst b/Changelog.rst
index 1bbaf8583d..40ef92fecc 100644
--- a/Changelog.rst
+++ b/Changelog.rst
@@ -1,10 +1,22 @@
 Version NEXTVERSION
 -------------------
 
-**2025-12-??**
-
+**2026-01-??**
+
+* New function to control the creation of cached elements during data
+  display: `cf.display_data`
+  (https://github.com/NCAS-CMS/cf-python/issues/913)
+* New methods: `cf.Data.get_cached_elements`
+  `cf.Data.cache_elements`
+  (https://github.com/NCAS-CMS/cf-python/issues/913)
+* Set cached elements during `cf.Data.__init__`
+  (https://github.com/NCAS-CMS/cf-python/issues/913)
+* Removed the `cf.constants.CONSTANTS` dictionary, replacing it
+  `cf.ConstantAccess.constants`
+  (https://github.com/NCAS-CMS/cf-python/issues/902)
 * Reduce the time taken to import `cf`
   (https://github.com/NCAS-CMS/cf-python/issues/902)
+* Changed dependency: ``cfdm>=1.12.4.0, <1.12.5.0``
 
 ----
 
diff --git a/cf/functions.py b/cf/functions.py
index f63b037305..7fa8a3d08a 100644
--- a/cf/functions.py
+++ b/cf/functions.py
@@ -156,6 +156,7 @@ def configuration(
     tempdir=None,
     chunksize=None,
     log_level=None,
+    display_data=None,
     regrid_logging=None,
     relaxed_identities=None,
     bounds_combination_mode=None,
@@ -177,6 +178,7 @@ def configuration(
     * `tempdir`
     * `chunksize`
     * `log_level`
+    * `display_data`
     * `regrid_logging`
     * `relaxed_identities`
     * `bounds_combination_mode`
@@ -200,10 +202,10 @@ def configuration(
     .. versionadded:: 3.6.0
 
     .. seealso:: `atol`, `rtol`, `tempdir`, `chunksize`,
-                 `total_memory`, `log_level`, `regrid_logging`,
-                 `relaxed_identities`, `bounds_combination_mode`,
-                 `active_storage`, `active_storage_url`,
-                 `active_storage_max_requests`
+                 `total_memory`, `log_level`, `display_data`,
+                 `regrid_logging`, `relaxed_identities`,
+                 `bounds_combination_mode`, `active_storage`,
+                 `active_storage_url`, `active_storage_max_requests`
 
     :Parameters:
 
@@ -245,6 +247,12 @@ def configuration(
             * ``'DETAIL'`` (``3``);
             * ``'DEBUG'`` (``-1``).
 
+        display_data `bool` or `Constant`, optional
+            The new display data option. The default is to not change
+            the current behaviour.
+
+            .. versionadded:: NEXTVERSION
+
         regrid_logging: `bool` or `Constant`, optional
             The new value (either True to enable logging or False to
             disable it). The default is to not change the current
@@ -303,6 +311,7 @@ def configuration(
      'log_level': 'WARNING',
      'bounds_combination_mode': 'AND',
      'chunksize': 82873466.88000001,
+     'display_data': True,
      'active_storage': False,
      'active_storage_url': None,
      'active_storage_max_requests': 100}
@@ -320,6 +329,7 @@ def configuration(
      'log_level': 'WARNING',
      'bounds_combination_mode': 'AND',
      'chunksize': 75000000.0,
+     'display_data': True,
      'active_storage': False,
      'active_storage_url': None,
      'active_storage_max_requests': 100}
@@ -347,6 +357,7 @@ def configuration(
      'log_level': 'INFO',
      'bounds_combination_mode': 'AND',
      'chunksize': 75000000.0,
+     'display_data': True,
      'active_storage': False,
      'active_storage_url': None}
     >>> with cf.configuration(atol=9, rtol=10):
@@ -360,6 +371,7 @@ def configuration(
      'log_level': 'INFO',
      'bounds_combination_mode': 'AND',
      'chunksize': 75000000.0,
+     'display_data': True,
      'active_storage': False,
      'active_storage_url': None,
      'active_storage_max_requests': 100}
@@ -372,6 +384,7 @@ def configuration(
      'log_level': 'INFO',
      'bounds_combination_mode': 'AND',
      'chunksize': 75000000.0,
+     'display_data': True,
      'active_storage': False,
      'active_storage_url': None,
      'active_storage_max_requests': 100}
@@ -402,6 +415,7 @@ def configuration(
         new_tempdir=tempdir,
         new_chunksize=chunksize,
         new_log_level=log_level,
+        new_display_data=display_data,
         new_regrid_logging=regrid_logging,
         new_relaxed_identities=relaxed_identities,
         bounds_combination_mode=bounds_combination_mode,
@@ -445,6 +459,7 @@ def _configuration(_Configuration, **kwargs):
         "new_tempdir": tempdir,
         "new_chunksize": chunksize,
         "new_log_level": log_level,
+        "new_display_data": display_data,
         "new_regrid_logging": regrid_logging,
         "new_relaxed_identities": relaxed_identities,
         "bounds_combination_mode": bounds_combination_mode,
@@ -459,10 +474,6 @@ def _configuration(_Configuration, **kwargs):
 
     old = ConstantAccess.constants(copy=True)
 
-    #    old = {name.lower(): val for name, val in CONSTANTS.items()}
-    #
-    #    old.pop("total_memory", None)
-
     # Filter out 'None' kwargs from configuration() defaults. Note that this
     # does not filter out '0' or 'True' values, which is important as the user
     # might be trying to set those, as opposed to None emerging as default.
@@ -552,7 +563,6 @@ def FREE_MEMORY():
 # Functions inherited from cfdm
 # --------------------------------------------------------------------
 class ConstantAccess(cfdm.ConstantAccess):
-    _constants = {}
     _Constant = Constant
 
     def __docstring_substitutions__(self):
@@ -576,6 +586,10 @@ class log_level(ConstantAccess, cfdm.log_level):
     _reset_log_emergence_level = _reset_log_emergence_level
 
 
+class display_data(ConstantAccess, cfdm.display_data):
+    pass
+
+
 class regrid_logging(ConstantAccess):
     """Whether or not to enable `esmpy` regridding logging.
 
diff --git a/cf/mixin/properties.py b/cf/mixin/properties.py
index dd7d80fa86..326c286678 100644
--- a/cf/mixin/properties.py
+++ b/cf/mixin/properties.py
@@ -7,8 +7,6 @@
     _DEPRECATION_ERROR_KWARGS,
     _DEPRECATION_ERROR_METHOD,
 )
-from ..functions import atol as cf_atol
-from ..functions import rtol as cf_rtol
 from ..mixin_container import Container
 from ..query import Query
 from ..units import Units
@@ -34,32 +32,6 @@ def __new__(cls, *args, **kwargs):
         instance._Data = Data
         return instance
 
-    # ----------------------------------------------------------------
-    # Private attributes
-    # ----------------------------------------------------------------
-    @property
-    def _atol(self):
-        """Return the tolerance on absolute differences between real
-        numbers, as returned by the `cf.atol` function.
-
-        This is used by, for example, the `_equals` method.
-
-        """
-        return cf_atol().value
-
-    @property
-    def _rtol(self):
-        """Return the tolerance on relative differences between real
-        numbers, as returned by the `cf.rtol` function.
-
-        This is used by, for example, the `_equals` method.
-
-        """
-        return cf_rtol().value
-
-    # ----------------------------------------------------------------
-    # Private methods
-    # ----------------------------------------------------------------
     def _matching_values(self, value0, value1, units=False, basic=False):
         """Whether two values match.
 
@@ -100,9 +72,6 @@ def _matching_values(self, value0, value1, units=False, basic=False):
 
             return self._equals(value1, value0, basic=basic)
 
-    # ----------------------------------------------------------------
-    # Attributes
-    # ----------------------------------------------------------------
     @property
     def id(self):
         """An identity for the {{class}} object.
@@ -150,9 +119,6 @@ def id(self):
                 f"{self.__class__.__name__} doesn't have attribute 'id'"
             )
 
-    # ----------------------------------------------------------------
-    # CF properties
-    # ----------------------------------------------------------------
     @property
     def calendar(self):
         """The calendar CF property.
@@ -554,9 +520,6 @@ def valid_range(self, value):
     def valid_range(self):
         self.del_property("valid_range", default=AttributeError())
 
-    # ----------------------------------------------------------------
-    # Methods
-    # ----------------------------------------------------------------
     def get_property(self, prop, default=ValueError()):
         """Get a CF property.
 
diff --git a/cf/mixin2/container.py b/cf/mixin2/container.py
index c5f0081462..44397301f4 100644
--- a/cf/mixin2/container.py
+++ b/cf/mixin2/container.py
@@ -6,7 +6,6 @@
 """
 
 from ..docstring import _docstring_substitution_definitions
-from ..functions import atol, rtol
 
 
 class Container:
@@ -55,23 +54,3 @@ def __docstring_package_depth__(self):
 
         """
         return 0
-
-    @property
-    def _atol(self):
-        """Internal alias for `{{package}}.atol`.
-
-        An alias is necessary to avoid a name clash with the keyword
-        argument of identical name (`atol`) in calling functions.
-
-        """
-        return atol().value
-
-    @property
-    def _rtol(self):
-        """Internal alias for `{{package}}.rtol`.
-
-        An alias is necessary to avoid a name clash with the keyword
-        argument of identical name (`rtol`) in calling functions.
-
-        """
-        return rtol().value
diff --git a/cf/test/test_Data.py b/cf/test/test_Data.py
index 2300a62e47..21bdff254d 100644
--- a/cf/test/test_Data.py
+++ b/cf/test/test_Data.py
@@ -1165,7 +1165,7 @@ def test_Data_concatenate(self):
         str(d)
         str(e)
         f = cf.Data.concatenate([d, e], axis=1)
-        cached = f._get_cached_elements()
+        cached = f.get_cached_elements()
         self.assertEqual(cached[0], d.first_element())
         self.assertEqual(cached[-1], e.last_element())
 
@@ -1205,7 +1205,7 @@ def test_Data_concatenate(self):
         repr(e)
         f = cf.Data.concatenate([d, e], axis=0)
         self.assertEqual(
-            f._get_cached_elements(),
+            f.get_cached_elements(),
             {0: d.first_element(), -1: e.last_element()},
         )
 
@@ -1709,6 +1709,12 @@ def test_Data_array(self):
         d = cf.Data([["2000-12-3 12:00"]], "days since 2000-12-01", dt=True)
         self.assertEqual(d.array, 2.5)
 
+        # Cached values
+        d = cf.Data([1, 2])
+        d._del_cached_elements()
+        d.array
+        self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 2})
+
     def test_Data_binary_mask(self):
         """Test the `binary_mask` Data property."""
         d = cf.Data([[0, 1, 2, 3.0]], "m")
@@ -3221,6 +3227,12 @@ def test_Data_compute(self):
         d = cf.Data([["2000-12-3 12:00"]], "days since 2000-12-01", dt=True)
         self.assertEqual(d.compute(), 2.5)
 
+        # Cached values
+        d = cf.Data([1, 2])
+        d._del_cached_elements()
+        d.compute()
+        self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 2})
+
     def test_Data_persist(self):
         """Test Data.persist."""
         d = cf.Data(9, "km")
@@ -4376,9 +4388,8 @@ def test_Data_Units(self):
 
         # Adjusted cached values
         d = cf.Data([1000, 2000, 3000], "m")
-        repr(d)
         d.Units = cf.Units("km")
-        self.assertEqual(d._get_cached_elements(), {0: 1.0, 1: 2.0, -1: 3.0})
+        self.assertEqual(d.get_cached_elements(), {0: 1.0, 1: 2.0, -1: 3.0})
 
     def test_Data_get_data(self):
         """Test the `get_data` Data method."""
@@ -4450,53 +4461,24 @@ def test_Data__str__(self):
         """Test `Data.__str__`"""
         elements0 = (0, -1, 1)
         for array in ([1], [1, 2], [1, 2, 3]):
-            elements = elements0[: len(array)]
-
             d = cf.Data(array)
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertNotIn(element, cache)
-
-            self.assertEqual(str(d), str(array))
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertIn(element, cache)
-
             d[0] = 1
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertNotIn(element, cache)
-
             self.assertEqual(str(d), str(array))
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertIn(element, cache)
-
             d += 0
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertNotIn(element, cache)
-
             self.assertEqual(str(d), str(array))
-            cache = d._get_cached_elements()
-            for element in elements:
-                self.assertIn(element, cache)
 
         # Test when size > 3, i.e. second element is not there.
         d = cf.Data([1, 2, 3, 4])
-        cache = d._get_cached_elements()
-        for element in elements0:
-            self.assertNotIn(element, cache)
 
         self.assertEqual(str(d), "[1, ..., 4]")
-        cache = d._get_cached_elements()
+        cache = d.get_cached_elements()
         self.assertNotIn(1, cache)
         for element in elements0[:2]:
             self.assertIn(element, cache)
 
         d[0] = 1
         for element in elements0:
-            self.assertNotIn(element, d._get_cached_elements())
+            self.assertNotIn(element, d.get_cached_elements())
 
     def test_Data_cull_graph(self):
         """Test Data.cull_graph."""
@@ -4703,6 +4685,135 @@ def test_Data_to_units(self):
         with self.assertRaises(ValueError):
             e.to_units("degC")
 
+    def test_Data_cache_elements(self):
+        """Test setting of cached elements."""
+        d = cf.Data(1)
+        self.assertEqual(d.get_cached_elements(), {0: 1, -1: 1})
+        self.assertIsNone(d._del_cached_elements())
+        self.assertFalse(d.get_cached_elements())
+
+        # Test via __init__, which calls `cache_elements`
+        for array in (np.ma.masked, True, "x"):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(
+                    d.get_cached_elements(), {0: array, -1: array}
+                )
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (
+            1,
+            1.0,
+            np.array(1),
+            np.array([1]),
+            [1],
+            (1,),
+        ):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(d.get_cached_elements(), {0: 1, -1: 1})
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (np.array([1, 2]), [1, 2]):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 2})
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (np.array([1, 2, 3]), (1, 2, 3)):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 3})
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (np.array([1, 2, 3, 4]), (1, 2, 3, 4)):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(d.get_cached_elements(), {0: 1, -1: 4})
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (np.array([[1, 2]]), [[1, 2]]):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(
+                    d.get_cached_elements(), {0: 1, 1: 2, -2: 1, -1: 2}
+                )
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        for array in (
+            np.array([[1, 2], [7, 8]]),
+            ([1, 2], [7, 8]),
+            np.array([[1, 2], [3, 4], [7, 8]]),
+            [[1, 2], [3, 4], [5, 6], [7, 8]],
+        ):
+            d = cf.Data(array)
+            for i in range(2):
+                self.assertEqual(
+                    d.get_cached_elements(), {0: 1, 1: 2, -2: 7, -1: 8}
+                )
+                # Check that getting the array doesn't change the
+                # cached elements
+                if i:
+                    d.array
+
+        # Sparse array
+        from scipy.sparse import csr_array
+
+        indptr = np.array([0, 2, 3, 6])
+        indices = np.array([0, 2, 2, 0, 1, 2])
+        data = np.array([1, 2, 3, 4, 5, 6])
+        array = csr_array((data, indices, indptr), shape=(3, 3))
+        d = cf.Data(array)
+        for i in range(2):
+            self.assertEqual(d.get_cached_elements(), {0: 1, -1: 6})
+            # Check that getting the array doesn't change the
+            # cached elements
+            if i:
+                d.array
+
+        # Check set_cached_elements
+        for array in ([1, 2, 3], [[1, 2, 3]]):
+            d = cf.Data(array)
+            d._del_cached_elements()
+            d.cache_elements()
+            self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 3})
+
+        # Check that __str__ sets missing cached elements
+        d = cf.Data([[1, 2, 3]])
+        d._del_cached_elements()
+        str(d)
+        self.assertEqual(d.get_cached_elements(), {0: 1, 1: 2, -1: 3})
+
+        # Interaction with `cf.display_data`
+        d = cf.Data([[1, 2, 3]])
+        d._del_cached_elements()
+        with cf.display_data(False):
+            self.assertEqual(repr(d), "<CF Data(1, 3): [[...]]>")
+
+        with cf.display_data(True):
+            self.assertEqual(repr(d), "<CF Data(1, 3): [[1, 2, 3]]>")
+
+        with cf.display_data(False):
+            self.assertEqual(repr(d), "<CF Data(1, 3): [[1, 2, 3]]>")
+
 
 if __name__ == "__main__":
     print("Run date:", datetime.datetime.now())
diff --git a/cf/test/test_functions.py b/cf/test/test_functions.py
index 1a26a1afdc..4ca7750e5f 100644
--- a/cf/test/test_functions.py
+++ b/cf/test/test_functions.py
@@ -55,7 +55,7 @@ def test_configuration(self):
         self.assertIsInstance(org, dict)
 
         # Check all keys that should be there are, with correct value type:
-        self.assertEqual(len(org), 11)  # update expected len if add new key(s)
+        self.assertEqual(len(org), 12)  # update expected len if add new key(s)
 
         # Types expected:
         self.assertIsInstance(org["atol"], float)
@@ -70,6 +70,7 @@ def test_configuration(self):
         # Log level may be input as an int but always given as
         # equiv. string
         self.assertIsInstance(org["log_level"], str)
+        self.assertIsInstance(org["display_data"], bool)
 
         # Store some sensible values to reset items to for testing, ensuring:
         # 1) they are kept different to the defaults (i.e. org values); and
diff --git a/docs/source/recipes/plot_08_recipe.py b/docs/source/recipes/plot_08_recipe.py
index 63427f62a7..6045f51448 100644
--- a/docs/source/recipes/plot_08_recipe.py
+++ b/docs/source/recipes/plot_08_recipe.py
@@ -9,11 +9,10 @@
 # 1. Import cf-python, cf-plot, numpy and scipy.stats:
 
 import cfplot as cfp
-import cf
-
 import numpy as np
 import scipy.stats as stats
 
+import cf
 
 # %%
 # 2. Three functions are defined:
diff --git a/docs/source/recipes/plot_12_recipe.py b/docs/source/recipes/plot_12_recipe.py
index b09db0b29f..5304194b19 100644
--- a/docs/source/recipes/plot_12_recipe.py
+++ b/docs/source/recipes/plot_12_recipe.py
@@ -13,8 +13,8 @@
 # %%
 # 1. Import cf-python, cf-plot and matplotlib.pyplot:
 
-import matplotlib.pyplot as plt
 import cfplot as cfp
+import matplotlib.pyplot as plt
 
 import cf
 
diff --git a/docs/source/recipes/plot_13_recipe.py b/docs/source/recipes/plot_13_recipe.py
index bf0398713e..9b658597d8 100644
--- a/docs/source/recipes/plot_13_recipe.py
+++ b/docs/source/recipes/plot_13_recipe.py
@@ -18,13 +18,11 @@
 # in next steps.
 
 import cartopy.crs as ccrs
-import matplotlib.patches as mpatches
-
 import cfplot as cfp
+import matplotlib.patches as mpatches
 
 import cf
 
-
 # %%
 # 2. Read and select the SST by index and look at its contents:
 sst = cf.read("~/recipes/ERA5_monthly_averaged_SST.nc")[0]
diff --git a/docs/source/recipes/plot_17_recipe.py b/docs/source/recipes/plot_17_recipe.py
index c94769e2ba..a66c90b518 100644
--- a/docs/source/recipes/plot_17_recipe.py
+++ b/docs/source/recipes/plot_17_recipe.py
@@ -11,8 +11,8 @@
 # %%
 # 1. Import cf-python and cf-plot:
 
-import matplotlib.pyplot as plt
 import cfplot as cfp
+import matplotlib.pyplot as plt
 
 import cf
 
diff --git a/docs/source/recipes/plot_18_recipe.py b/docs/source/recipes/plot_18_recipe.py
index f0eae36e35..3beb9d0db9 100644
--- a/docs/source/recipes/plot_18_recipe.py
+++ b/docs/source/recipes/plot_18_recipe.py
@@ -10,15 +10,15 @@
 
 """
 
+import cfplot as cfp
+
 # %%
 # 1. Import cf-python, cf-plot and other required packages:
 import matplotlib.pyplot as plt
 import scipy.stats.mstats as mstats
-import cfplot as cfp
 
 import cf
 
-
 # %%
 # 2. Read the data in and unpack the Fields from FieldLists using indexing.
 # In our example We are investigating the influence of the land height on
diff --git a/docs/source/recipes/plot_19_recipe.py b/docs/source/recipes/plot_19_recipe.py
index 02d493dc21..ceb9db1c5c 100644
--- a/docs/source/recipes/plot_19_recipe.py
+++ b/docs/source/recipes/plot_19_recipe.py
@@ -9,10 +9,11 @@
 maxima.
 """
 
+import cfplot as cfp
+
 # %%
 # 1. Import cf-python, cf-plot and other required packages:
 import matplotlib.pyplot as plt
-import cfplot as cfp
 
 import cf
 
diff --git a/docs/source/recipes/plot_22_recipe.py b/docs/source/recipes/plot_22_recipe.py
index 377313c899..fe329cda9d 100644
--- a/docs/source/recipes/plot_22_recipe.py
+++ b/docs/source/recipes/plot_22_recipe.py
@@ -11,10 +11,11 @@
 # %%
 # 1. Import cf-python, Dask.array, NumPy, and Matplotlib:
 
-import cf
 import dask.array as da
-import numpy as np
 import matplotlib.pyplot as plt
+import numpy as np
+
+import cf
 
 # %%
 # 2. Read the field constructs and load the wind speed component fields:
diff --git a/docs/source/recipes/plot_23_recipe.py b/docs/source/recipes/plot_23_recipe.py
index 2499b0d875..29537803af 100644
--- a/docs/source/recipes/plot_23_recipe.py
+++ b/docs/source/recipes/plot_23_recipe.py
@@ -18,12 +18,12 @@
 # sphinx_gallery_thumbnail_number = 2
 # sphinx_gallery_end_ignore
 
-import matplotlib.pyplot as plt
 import cfplot as cfp
-import cf
-
-import numpy as np
 import dask.array as da
+import matplotlib.pyplot as plt
+import numpy as np
+
+import cf
 
 # %%
 # 2. Read example data field constructs, and set region for our plots: