diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index fc8e848bb..aeb62b9b0 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -126,26 +126,18 @@ This allows people to (1) use PyBaMM without importing optional dependencies by
 
 **Writing Tests for Optional Dependencies**
 
-Whenever a new optional dependency is added for optional functionality, it is recommended to write a corresponding unit test in `test_util.py`. This ensures that an error is raised upon the absence of said dependency. Here's an example:
+Below, we list the currently available test functions to provide an overview. If you find it useful to add new test cases please do so within `tests/unit/test_util.py`.
 
-```python
-from tests import TestCase
-import pybamm
-
-
-class TestUtil(TestCase):
-    def test_optional_dependency(self):
-        # Test that an error is raised when pybtex is not available
-        with self.assertRaisesRegex(
-            ModuleNotFoundError, "Optional dependency pybtex is not available"
-        ):
-            sys.modules["pybtex"] = None
-            pybamm.function_using_pybtex(x, y, z)
-
-        # Test that the function works when pybtex is available
-        sys.modules["pybtex"] = pybamm.util.import_optional_dependency("pybtex")
-        pybamm.function_using_pybtex(x, y, z)
-```
+Currently, there are three functions to test what concerns optional dependencies:
+- `test_import_optional_dependency`
+- `test_pybamm_import`
+- `test_optional_dependencies`
+
+The `test_import_optional_dependency` function extracts the optional dependencies installed in the setup environment, makes them unimportable (by setting them to `None` among the `sys.modules`), and tests that the `pybamm.util.import_optional_dependency` function throws a `ModuleNotFoundError` exception when their import is attempted.
+
+The `test_pybamm_import` function extracts the optional dependencies installed in the setup environment and makes them unimportable (by setting them to `None` among the `sys.modules`), unloads `pybamm` and its sub-modules, and finally tests that `pybamm` can be imported successfully. In fact, it is essential that the `pybamm` package is importable with only the mandatory dependencies.
+
+The `test_optional_dependencies` function extracts `pybamm` mandatory distribution packages and verifies that they are not present in the optional distribution packages list in `pyproject.toml`. This test is crucial for ensuring the consistency of the released package information and potential updates to dependencies during development.
 
 ## Testing
 
diff --git a/pybamm/citations.py b/pybamm/citations.py
index ff1851bfa..ae18f9adc 100644
--- a/pybamm/citations.py
+++ b/pybamm/citations.py
@@ -67,29 +67,41 @@ class Citations:
         """Reads the citations in `pybamm.CITATIONS.bib`. Other works can be cited
         by passing a BibTeX citation to :meth:`register`.
         """
-        parse_file = import_optional_dependency("pybtex.database", "parse_file")
-        citations_file = os.path.join(pybamm.root_dir(), "pybamm", "CITATIONS.bib")
-        bib_data = parse_file(citations_file, bib_format="bibtex")
-        for key, entry in bib_data.entries.items():
-            self._add_citation(key, entry)
+        try:
+            parse_file = import_optional_dependency("pybtex.database", "parse_file")
+            citations_file = os.path.join(pybamm.root_dir(), "pybamm", "CITATIONS.bib")
+            bib_data = parse_file(citations_file, bib_format="bibtex")
+            for key, entry in bib_data.entries.items():
+                self._add_citation(key, entry)
+        except ModuleNotFoundError:  # pragma: no cover
+            pybamm.logger.warning(
+                "Citations could not be read because the 'pybtex' library is not installed. "
+                "Install 'pybamm[cite]' to enable citation reading."
+            )
 
     def _add_citation(self, key, entry):
         """Adds `entry` to `self._all_citations` under `key`, warning the user if a
         previous entry is overwritten
         """
 
-        Entry = import_optional_dependency("pybtex.database", "Entry")
-        # Check input types are correct
-        if not isinstance(key, str) or not isinstance(entry, Entry):
-            raise TypeError()
-
-        # Warn if overwriting a previous citation
-        new_citation = entry.to_string("bibtex")
-        if key in self._all_citations and new_citation != self._all_citations[key]:
-            warnings.warn(f"Replacing citation for {key}", stacklevel=2)
-
-        # Add to database
-        self._all_citations[key] = new_citation
+        try:
+            Entry = import_optional_dependency("pybtex.database", "Entry")
+            # Check input types are correct
+            if not isinstance(key, str) or not isinstance(entry, Entry):
+                raise TypeError()
+
+            # Warn if overwriting a previous citation
+            new_citation = entry.to_string("bibtex")
+            if key in self._all_citations and new_citation != self._all_citations[key]:
+                warnings.warn(f"Replacing citation for {key}", stacklevel=2)
+
+            # Add to database
+            self._all_citations[key] = new_citation
+        except ModuleNotFoundError:  # pragma: no cover
+            pybamm.logger.warning(
+                f"Could not add citation for '{key}' because the 'pybtex' library is not installed. "
+                "Install 'pybamm[cite]' to enable adding citations."
+            )
 
     def _add_citation_tag(self, key, entry):
         """Adds a tag for a citation key in the dict, which represents the name of the
@@ -143,24 +155,32 @@ class Citations:
         key: str
             A BibTeX formatted citation
         """
-        PybtexError = import_optional_dependency("pybtex.scanner", "PybtexError")
-        parse_string = import_optional_dependency("pybtex.database", "parse_string")
         try:
-            # Parse string as a bibtex citation, and check that a citation was found
-            bib_data = parse_string(key, bib_format="bibtex")
-            if not bib_data.entries:
-                raise PybtexError("no entries found")
-
-            # Add and register all citations
-            for key, entry in bib_data.entries.items():
-                # Add to _all_citations dictionary
-                self._add_citation(key, entry)
-                # Add to _papers_to_cite set
-                self._papers_to_cite.add(key)
-                return
-        except PybtexError as error:
-            # Unable to parse / unknown key
-            raise KeyError(f"Not a bibtex citation or known citation: {key}") from error
+            PybtexError = import_optional_dependency("pybtex.scanner", "PybtexError")
+            parse_string = import_optional_dependency("pybtex.database", "parse_string")
+            try:
+                # Parse string as a bibtex citation, and check that a citation was found
+                bib_data = parse_string(key, bib_format="bibtex")
+                if not bib_data.entries:
+                    raise PybtexError("no entries found")
+
+                # Add and register all citations
+                for key, entry in bib_data.entries.items():
+                    # Add to _all_citations dictionary
+                    self._add_citation(key, entry)
+                    # Add to _papers_to_cite set
+                    self._papers_to_cite.add(key)
+                    return
+            except PybtexError as error:
+                # Unable to parse / unknown key
+                raise KeyError(
+                    f"Not a bibtex citation or known citation: {key}"
+                ) from error
+        except ModuleNotFoundError:  # pragma: no cover
+            pybamm.logger.warning(
+                f"Could not parse citation for '{key}' because the 'pybtex' library is not installed. "
+                "Install 'pybamm[cite]' to enable citation parsing."
+            )
 
     def _tag_citations(self):
         """Prints the citation tags for the citations that have been registered
@@ -211,38 +231,44 @@ class Citations:
         """
         # Parse citations that were not known keys at registration, but do not
         # fail if they cannot be parsed
-        pybtex = import_optional_dependency("pybtex")
         try:
-            for key in self._unknown_citations:
-                self._parse_citation(key)
-        except KeyError:  # pragma: no cover
-            warnings.warn(
-                message=f'\nCitation with key "{key}" is invalid. Please try again\n',
-                category=UserWarning,
-                stacklevel=2,
-            )
-            # delete the invalid citation from the set
-            self._unknown_citations.remove(key)
-
-        if output_format == "text":
-            citations = pybtex.format_from_strings(
-                self._cited, style="plain", output_backend="plaintext"
+            pybtex = import_optional_dependency("pybtex")
+            try:
+                for key in self._unknown_citations:
+                    self._parse_citation(key)
+            except KeyError:  # pragma: no cover
+                warnings.warn(
+                    message=f'\nCitation with key "{key}" is invalid. Please try again\n',
+                    category=UserWarning,
+                    stacklevel=2,
+                )
+                # delete the invalid citation from the set
+                self._unknown_citations.remove(key)
+
+            if output_format == "text":
+                citations = pybtex.format_from_strings(
+                    self._cited, style="plain", output_backend="plaintext"
+                )
+            elif output_format == "bibtex":
+                citations = "\n".join(self._cited)
+            else:
+                raise pybamm.OptionError(
+                    f"Output format {output_format} not recognised."
+                    "It should be 'text' or 'bibtex'."
+                )
+
+            if filename is None:
+                print(citations)
+                if verbose:
+                    self._tag_citations()  # pragma: no cover
+            else:
+                with open(filename, "w") as f:
+                    f.write(citations)
+        except ModuleNotFoundError:  # pragma: no cover
+            pybamm.logger.warning(
+                "Could not print citations because the 'pybtex' library is not installed. "
+                "Please, install 'pybamm[cite]' to print citations."
             )
-        elif output_format == "bibtex":
-            citations = "\n".join(self._cited)
-        else:
-            raise pybamm.OptionError(
-                f"Output format {output_format} not recognised."
-                "It should be 'text' or 'bibtex'."
-            )
-
-        if filename is None:
-            print(citations)
-            if verbose:
-                self._tag_citations()  # pragma: no cover
-        else:
-            with open(filename, "w") as f:
-                f.write(citations)
 
 
 def print_citations(filename=None, output_format="text", verbose=False):

diff --git a/tests/unit/test_util.py b/tests/unit/test_util.py
index 3d6fafdd6..603af5056 100644
--- a/tests/unit/test_util.py
+++ b/tests/unit/test_util.py
@@ -93,7 +93,7 @@ class TestUtil(TestCase):
             "pybamm", optional_distribution_deps=optional_distribution_deps
         )
 
-        # Save optional dependencies, then set to None
+        # Save optional dependencies, then make them not importable
         modules = {}
         for import_pkg in present_optional_import_deps:
             modules[import_pkg] = sys.modules.get(import_pkg)
@@ -117,23 +117,31 @@ class TestUtil(TestCase):
             "pybamm", optional_distribution_deps=optional_distribution_deps
         )
 
-        # Save optional dependencies, then set to None
+        # Save optional dependencies and their sub-modules, then make them not importable
         modules = {}
-        for import_pkg in present_optional_import_deps:
-            modules[import_pkg] = sys.modules.get(import_pkg)
-            sys.modules[import_pkg] = None
+        for module_name, module in sys.modules.items():
+            base_module_name = module_name.split(".")[0]
+            if base_module_name in present_optional_import_deps:
+                modules[module_name] = module
+                sys.modules[module_name] = None
+
+        # Unload pybamm and its sub-modules
+        for module_name in list(sys.modules.keys()):
+            base_module_name = module_name.split(".")[0]
+            if base_module_name == "pybamm":
+                sys.modules.pop(module_name)
 
         # Test pybamm is still importable
         try:
-            importlib.reload(importlib.import_module("pybamm"))
+            importlib.import_module("pybamm")
         except ModuleNotFoundError as error:
             self.fail(
                 f"Import of 'pybamm' shouldn't require optional dependencies. Error: {error}"
             )
-
-        # Restore optional dependencies
-        for import_pkg in present_optional_import_deps:
-            sys.modules[import_pkg] = modules[import_pkg]
+        finally:
+            # Restore optional dependencies and their sub-modules
+            for module_name, module in modules.items():
+                sys.modules[module_name] = module
 
     def test_optional_dependencies(self):
         optional_distribution_deps = get_optional_distribution_deps("pybamm")

PyBaMM import error - Cannot run anything (import broken due to `pybtex`)
### Discussed in https://github.com/pybamm-team/PyBaMM/discussions/3928

<div type='discussions-op-text'>

<sup>Originally posted by **abhishek-appana** March 25, 2024</sup>
Hello,

I am running Python 3.11.8 and installed PyBaMM 24.1 using pip on a Windows system. Earlier I was using Python 3.10 and everything was fine. But I am getting the below error after upgrading Python.

When I run `import pybamm`, it gives me the error:

ModuleNotFoundError: Optional dependency pybtex.database is not available. See https://docs.pybamm.org/en/latest/source/user_guide/installation/index.html#optional-dependencies for more details.

I tried installing pybamm using `pip install pybamm[all]`. I was still getting this error. How do I resolve this?</div>

<hr>

I think that this is a valid bug and it is still failing, and `import pybamm` should work without installing `pybamm[all]`. It can be noticed in the logs here: https://github.com/pybamm-team/PyBaMM/actions/runs/8461852686/job/23182296194, so I've converted this discussion to an issue instead (cc: @Saransh-cpp @arjxn-py). 

Perhaps this isn't being properly checked through #3892, @lorenzofavaro?
tests/unit/test_util.py::TestUtil::test_is_jax_compatible tests/unit/test_util.py::TestSearch::test_url_gets_to_stdout tests/unit/test_util.py::TestUtil::test_get_parameters_filepath tests/unit/test_util.py::TestUtil::test_fuzzy_dict tests/unit/test_util.py::TestUtil::test_is_constant_and_can_evaluate tests/unit/test_util.py::TestUtil::test_git_commit_info tests/unit/test_util.py::TestUtil::test_optional_dependencies tests/unit/test_util.py::TestUtil::test_import_optional_dependency tests/unit/test_util.py::TestUtil::test_pybamm_import