diff --git a/petsctools/__init__.py b/petsctools/__init__.py
index a2f1bae..acb869d 100644
--- a/petsctools/__init__.py
+++ b/petsctools/__init__.py
@@ -11,7 +11,9 @@
 from .options import flatten_parameters  # noqa: F401
 from .utils import PETSC4PY_INSTALLED
 
-# Now conditionally import the functions that depend on petsc4py
+# Now conditionally import the functions that depend on petsc4py. If petsc4py
+# is not available then attempting to access these attributes will raise an
+# informative error.
 if PETSC4PY_INSTALLED:
     from .config import get_blas_library  # noqa: F401
     from .init import (  # noqa: F401
@@ -30,3 +32,32 @@
         is_set_from_options,
         inserted_options,
     )
+else:
+
+    def __getattr__(name):
+        petsc4py_attrs = {
+            "get_blas_library",
+            "InvalidEnvironmentException",
+            "InvalidPetscVersionException",
+            "init",
+            "get_commandline_options",
+            "OptionsManager",
+            "petscobj2str",
+            "attach_options",
+            "has_options",
+            "get_options",
+            "set_from_options",
+            "is_set_from_options",
+            "inserted_options",
+        }
+        if name in petsc4py_attrs:
+            raise ImportError(
+                f"Cannot load '{name}' from module '{__name__}' because "
+                "petsc4py is not available.\n"
+                "If this error appears during pip install then you may have "
+                "forgotten to pass --no-build-isolation"
+            )
+        else:
+            raise AttributeError(
+                f"Module '{__name__}' has no attribute '{name}'"
+            )
diff --git a/tests/conftest.py b/tests/conftest.py
index a75ee2d..f625af9 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -2,6 +2,10 @@
 
 
 def pytest_configure(config):
+    config.addinivalue_line(
+        "markers",
+        "skippetsc4py: mark as skipped unless petsc4py is not installed",
+    )
     config.addinivalue_line(
         "markers",
         "skipnopetsc4py: mark as skipped unless petsc4py is installed",
@@ -17,6 +21,14 @@ def pytest_collection_modifyitems(session, config, items):
         petsc4py_installed = False
 
     for item in items:
+        if (
+            item.get_closest_marker("skippetsc4py") is not None
+            and petsc4py_installed
+        ):
+            item.add_marker(
+                pytest.mark.skip(reason="Test requires not having petsc4py")
+            )
+
         if (
             item.get_closest_marker("skipnopetsc4py") is not None
             and not petsc4py_installed
diff --git a/tests/test_no_petsc4py.py b/tests/test_no_petsc4py.py
new file mode 100644
index 0000000..cfc7a8e
--- /dev/null
+++ b/tests/test_no_petsc4py.py
@@ -0,0 +1,14 @@
+import petsctools
+import pytest
+
+
+@pytest.mark.skippetsc4py
+def test_import_error_raised_when_petsc4py_unavailable():
+    with pytest.raises(ImportError):
+        petsctools.init()
+
+    with pytest.raises(ImportError):
+        petsctools.OptionsManager({}, "prefix")
+
+    with pytest.raises(ImportError):
+        petsctools.get_blas_library()