diff --git a/Changelog.rst b/Changelog.rst
index c5dba1d851..40c1faee1c 100644
--- a/Changelog.rst
+++ b/Changelog.rst
@@ -7,6 +7,9 @@ version NEXT
 * Fix for zero-sized unlimited dimensions when read from a grouped
   netCDF file (https://github.com/NCAS-CMS/cfdm/issues/113)
 * Performance enhancements (https://github.com/NCAS-CMS/cfdm/issues/124)
+* Better error message in the case of a `numpy.ma.core.MaskError` occurring
+  upon reading of CDL files with only header or coordinate information
+  (https://github.com/NCAS-CMS/cfdm/issues/128)
 * Changed dependency: ``cftime>=1.4.1``
 * Changed dependency: ``netCDF4>=1.5.4``
 
diff --git a/cfdm/read_write/read.py b/cfdm/read_write/read.py
index e4026903ea..9b2b3297f0 100644
--- a/cfdm/read_write/read.py
+++ b/cfdm/read_write/read.py
@@ -1,5 +1,7 @@
 import os
 
+from numpy.ma.core import MaskError
+
 from ..cfdmimplementation import implementation
 
 from .netcdf import NetCDFRead
@@ -299,16 +301,34 @@ def read(
         filename = netcdf.cdl_to_netcdf(filename)
 
     if netcdf.is_netcdf_file(filename):
-        fields = netcdf.read(
-            filename,
-            external=external,
-            extra=extra,
-            verbose=verbose,
-            warnings=warnings,
-            warn_valid=warn_valid,
-            mask=mask,
-            extra_read_vars=None,
-        )
+        # See https://github.com/NCAS-CMS/cfdm/issues/128 for context on the
+        # try/except here, which acts as a temporary fix pending decisions on
+        # the best way to handle CDL with only header or coordinate info.
+        try:
+            fields = netcdf.read(
+                filename,
+                external=external,
+                extra=extra,
+                verbose=verbose,
+                warnings=warnings,
+                warn_valid=warn_valid,
+                mask=mask,
+                extra_read_vars=None,
+            )
+        except MaskError:
+            # Some data required for field interpretation is missing,
+            # manifesting downstream as a NumPy MaskError.
+            if cdl:
+                raise ValueError(
+                    "Unable to convert CDL without data to field construct(s) "
+                    "because there is insufficient information provided by "
+                    "the header and/or coordinates alone in this case."
+                )
+            else:
+                raise ValueError(
+                    "Unable to convert netCDF to field construct(s) because "
+                    "there is missing data."
+                )
     elif cdl:
         raise IOError(
             "Can't determine format of file {} "
diff --git a/cfdm/test/test_read_write.py b/cfdm/test/test_read_write.py
index a5dc1d13ec..4f2a92074e 100644
--- a/cfdm/test/test_read_write.py
+++ b/cfdm/test/test_read_write.py
@@ -18,7 +18,7 @@
 warnings = False
 
 # Set up temporary files
-n_tmpfiles = 6
+n_tmpfiles = 8
 tmpfiles = [
     tempfile.mkstemp("_test_read_write.nc", dir=os.getcwd())[1]
     for i in range(n_tmpfiles)
@@ -27,7 +27,9 @@
     tmpfile,
     tmpfileh,
     tmpfileh2,
+    tmpfileh3,
     tmpfilec,
+    tmpfilec2,
     tmpfile0,
     tmpfile1,
 ) = tmpfiles
@@ -336,6 +338,11 @@ def test_read_CDL(self):
             shell=True,
             check=True,
         )
+
+        # For the cases of '-h' and '-c', i.e. only header info or coordinates,
+        # notably no data, take two cases each: one where there is sufficient
+        # info from the metadata to map to fields, and one where there isn't:
+        #     1. Sufficient metadata, so should be read-in successfully
         subprocess.run(
             " ".join(["ncdump", "-h", self.filename, ">", tmpfileh]),
             shell=True,
@@ -347,11 +354,35 @@ def test_read_CDL(self):
             check=True,
         )
 
+        #     2. Insufficient metadata, so should error with a message as such
+        geometry_1_file = os.path.join(
+            os.path.dirname(os.path.abspath(__file__)), "geometry_1.nc"
+        )
+        subprocess.run(
+            " ".join(["ncdump", "-h", geometry_1_file, ">", tmpfileh2]),
+            shell=True,
+            check=True,
+        )
+        subprocess.run(
+            " ".join(["ncdump", "-c", geometry_1_file, ">", tmpfilec2]),
+            shell=True,
+            check=True,
+        )
+
         f0 = cfdm.read(self.filename)[0]
+
+        # Case (1) as above, so read in and check the fields are as should be
         f = cfdm.read(tmpfile)[0]
         cfdm.read(tmpfileh)[0]
         c = cfdm.read(tmpfilec)[0]
 
+        # Case (2) as above, so the right error should be raised on read
+        with self.assertRaises(ValueError):
+            cfdm.read(tmpfileh2)[0]
+
+        with self.assertRaises(ValueError):
+            cfdm.read(tmpfilec2)[0]
+
         self.assertTrue(f0.equals(f, verbose=3))
 
         self.assertTrue(
@@ -391,10 +422,10 @@ def test_read_CDL(self):
                             "-e",
                             regex,
                             tmpfileh,
-                            ">" + tmpfileh2,
+                            ">" + tmpfileh3,
                             "&&",
                             "mv",
-                            tmpfileh2,
+                            tmpfileh3,
                             tmpfileh,
                         ]
                     ),