diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index b76189b..6f8a9af 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -9,6 +9,9 @@ on:
     tags:
       - 'v*'
   pull_request:
+  # Run weekly to check for breaking changes in unpinned dependencies
+  schedule:
+    - cron: '0 18 * * 5'
 
 jobs:
 
@@ -18,8 +21,6 @@ jobs:
     strategy:
       matrix:
         python-version: ["3.7", "3.8", "3.9", "3.10"]
-        sphinx: [">=3,<4", ">=5,<6"]
-        pygments: ["==2.8.0", "==2.9.0", "==2.12.0",]
 
     steps:
     - uses: actions/checkout@v2
@@ -30,17 +31,15 @@ jobs:
     - name: Install dependencies
       run: |
         python -m pip install --upgrade pip
-        pip install "sphinx${{ matrix.sphinx }}"
-        pip install "pygments${{ matrix.pygments }}"
         pip install .[testing]
     - name: Run pytest
       run: |
         pytest --cov=sphinx_tabs --cov-report=xml --cov-report=term-missing
     - name: Upload to Codecov
-      if: matrix.python-version == 3.7 && matrix.sphinx == '>=3,<4' && github.repository == 'executablebooks/sphinx-tabs'
+      if: matrix.python-version == '3.10' && github.repository == 'executablebooks/sphinx-tabs'
       uses: codecov/codecov-action@v1
       with:
-        name: sphinx-tabs-pytests-py3.7
+        name: sphinx-tabs-pytests-py3.10
         flags: pytests
         file: ./coverage.xml
         fail_ci_if_error: true
diff --git a/setup.py b/setup.py
index 81267ed..ba91c96 100755
--- a/setup.py
+++ b/setup.py
@@ -25,7 +25,7 @@ def get_version():
     url="https://github.com/executablebooks/sphinx-tabs",
     license="MIT",
     python_requires="~=3.7",
-    install_requires=["sphinx>=2,<6", "pygments", "docutils~=0.17.0", "jinja2<3.1.0"],
+    install_requires=["sphinx", "pygments", "docutils~=0.18.0"],
     extras_require={
         "testing": [
             "coverage",
diff --git a/tests/test_build.py b/tests/test_build.py
index 2e32014..4a21690 100644
--- a/tests/test_build.py
+++ b/tests/test_build.py
@@ -28,10 +28,6 @@ def test_conditional_assets(app, docname, check_asset_links):
 @pytest.mark.noautobuild
 @pytest.mark.parametrize("docname", ["index", "no_tabs1", "no_tabs2"])
 @pytest.mark.sphinx(testroot="conditionalassets-policy")
-@pytest.mark.skipif(
-    sphinx.version_info[:2] < (4, 1),
-    reason="Test uses option that was introduced in Sphinx 4.1 ",
-)
 def test_conditional_assets_html_assets_policy(
     app,
     docname,
@@ -56,21 +52,10 @@ def test_conditional_assets_html_assets_policy(
 
 
 @pytest.mark.sphinx(testroot="linenos")
-@pytest.mark.skipif(
-    sphinx.version_info[:2] >= (4, 0), reason="Test uses Sphinx 3 code blocks"
-)
 def test_other_with_assets(app, check_asset_links):
     check_asset_links(app)
 
 
-@pytest.mark.sphinx(testroot="linenos")
-@pytest.mark.skipif(
-    sphinx.version_info[:2] < (4, 0), reason="Test uses Sphinx 4 code blocks"
-)
-def test_other_with_assets_new_style(app, check_asset_links):
-    check_asset_links(app)
-
-
 @pytest.mark.sphinx(testroot="nestedmarkup")
 def test_nested_markup(app, check_asset_links):
     check_asset_links(app)
diff --git a/tests/test_build/test_other_with_assets.html b/tests/test_build/test_other_with_assets.html
index 7f5c9df..85b55c4 100644
--- a/tests/test_build/test_other_with_assets.html
+++ b/tests/test_build/test_other_with_assets.html
@@ -12,17 +12,6 @@
     </div>
     <div aria-labelledby="tab-0-Qysr" class="sphinx-tabs-panel code-tab group-tab" id="panel-0-Qysr" name="Qysr" role="tabpanel" tabindex="0">
      <div class="highlight-c++ notranslate">
-      <table class="highlighttable">
-       <tr>
-        <td class="linenos">
-         <div class="linenodiv">
-          <pre><span class="normal">1</span></pre>
-         </div>
-        </td>
-        <td class="code">
-        </td>
-       </tr>
-      </table>
      </div>
     </div>
     <div aria-labelledby="tab-0-UHl0aG9u" class="sphinx-tabs-panel code-tab group-tab" hidden="true" id="panel-0-UHl0aG9u" name="UHl0aG9u" role="tabpanel" tabindex="0">
diff --git a/tests/test_build/test_other_with_assets_new_style.html b/tests/test_build/test_other_with_assets_new_style.html
deleted file mode 100644
index 85b55c4..0000000
--- a/tests/test_build/test_other_with_assets_new_style.html
+++ /dev/null
@@ -1,24 +0,0 @@
-<div class="documentwrapper">
- <div class="bodywrapper">
-  <div class="body" role="main">
-   <div class="sphinx-tabs docutils container">
-    <div aria-label="Tabbed content" class="closeable" role="tablist">
-     <button aria-controls="panel-0-Qysr" aria-selected="true" class="sphinx-tabs-tab code-tab group-tab" id="tab-0-Qysr" name="Qysr" role="tab" tabindex="0">
-      C++
-     </button>
-     <button aria-controls="panel-0-UHl0aG9u" aria-selected="false" class="sphinx-tabs-tab code-tab group-tab" id="tab-0-UHl0aG9u" name="UHl0aG9u" role="tab" tabindex="-1">
-      Python
-     </button>
-    </div>
-    <div aria-labelledby="tab-0-Qysr" class="sphinx-tabs-panel code-tab group-tab" id="panel-0-Qysr" name="Qysr" role="tabpanel" tabindex="0">
-     <div class="highlight-c++ notranslate">
-     </div>
-    </div>
-    <div aria-labelledby="tab-0-UHl0aG9u" class="sphinx-tabs-panel code-tab group-tab" hidden="true" id="panel-0-UHl0aG9u" name="UHl0aG9u" role="tabpanel" tabindex="0">
-     <div class="highlight-python notranslate">
-     </div>
-    </div>
-   </div>
-  </div>
- </div>
-</div>
diff --git a/tests/test_build/test_other_with_assets_new_style.xml b/tests/test_build/test_other_with_assets_new_style.xml
deleted file mode 100644
index 6d286b9..0000000
--- a/tests/test_build/test_other_with_assets_new_style.xml
+++ /dev/null
@@ -1,13 +0,0 @@
-<document source="index.rst">
-    <container classes="sphinx-tabs" type="tab-element">
-        <div aria-label="Tabbed content" classes="closeable" role="tablist">
-            <button aria-controls="panel-0-Qysr" aria-selected="true" classes="sphinx-tabs-tab code-tab group-tab" ids="tab-0-Qysr" name="Qysr" role="tab" tabindex="0">
-                C++
-            <button aria-controls="panel-0-UHl0aG9u" aria-selected="false" classes="sphinx-tabs-tab code-tab group-tab" ids="tab-0-UHl0aG9u" name="UHl0aG9u" role="tab" tabindex="-1">
-                Python
-        <div aria-labelledby="tab-0-Qysr" classes="sphinx-tabs-panel code-tab group-tab" ids="panel-0-Qysr" name="Qysr" role="tabpanel" tabindex="0">
-            <literal_block force="False" highlight_args="{}" language="c++" linenos="True" xml:space="preserve">
-                std::cout << "hello world" << std::endl;
-        <div aria-labelledby="tab-0-UHl0aG9u" classes="sphinx-tabs-panel code-tab group-tab" hidden="true" ids="panel-0-UHl0aG9u" name="UHl0aG9u" role="tabpanel" tabindex="0">
-            <literal_block force="False" highlight_args="{}" language="python" xml:space="preserve">
-                print('hello world')