diff --git a/Dockerfile b/Dockerfile
index cb990269..051b2757 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -35,11 +35,18 @@ COPY --link scripts/build_python.sh /
 
 # ------------------------------------------------------------------------------
 FROM builder-py-base as builder-py-3_12
-RUN /build_python.sh 3.12.5
+RUN /build_python.sh 3.12.7
 # ------------------------------------------------------------------------------
 FROM builder-py-base as builder-py-3_13
 RUN /build_python.sh 3.13.0rc3
 # ------------------------------------------------------------------------------
+FROM builder-py-base as builder-py-3_13t
+# Building with all 3 of the options below causes tests to fail.
+# Removing just the first means the image is a bit bigger, but we keep optimisations
+# --disable-test-modules --enable-optimizations --with-lto
+ENV PYTHON_CONFIGURE_OPTS='--enable-optimizations --with-lto --with-system-expat --without-ensurepip'
+RUN /build_python.sh 3.13.0rc3t
+# ------------------------------------------------------------------------------
 FROM python:3.12-slim-bookworm as base
 
 ENV PIP_DISABLE_PIP_VERSION_CHECK=1 \
@@ -56,6 +63,7 @@ RUN apt-get -y update \
 COPY --link --from=builder-nsjail /nsjail/nsjail /usr/sbin/
 COPY --link --from=builder-py-3_12 /snekbin/ /snekbin/
 COPY --link --from=builder-py-3_13 /snekbin/ /snekbin/
+COPY --link --from=builder-py-3_13t /snekbin/ /snekbin/
 
 RUN chmod +x /usr/sbin/nsjail \
     && ln -s /snekbin/python/3.12/ /snekbin/python/default
diff --git a/requirements/eval-deps.pip b/requirements/eval-deps.pip
index 45496d70..d18948c7 100644
--- a/requirements/eval-deps.pip
+++ b/requirements/eval-deps.pip
@@ -7,7 +7,7 @@ fishhook~=0.3; python_version == '3.12'
 forbiddenfruit~=0.1
 fuzzywuzzy~=0.18
 lark~=1.2
-matplotlib~=3.9
+matplotlib~=3.9 ; python_version != '3.13'
 more-itertools~=10.5
 networkx~=3.3
 numpy~=2.1
@@ -16,7 +16,7 @@ pendulum~=3.0 ; python_version == '3.12'
 pyarrow~=17.0; python_version == '3.12'
 python-dateutil~=2.9
 pyyaml~=6.0
-scipy~=1.14
+scipy~=1.14 ; python_version != '3.13'
 sympy~=1.13
 typing-extensions~=4.12
 tzdata~=2024.2
diff --git a/scripts/build_python.sh b/scripts/build_python.sh
index 77f50ab6..d026eb89 100755
--- a/scripts/build_python.sh
+++ b/scripts/build_python.sh
@@ -4,11 +4,19 @@ shopt -s inherit_errexit
 
 py_version="${1}"
 
-# Install Python interpreter under e.g. /snekbin/python/3.11/ (no patch version).
+# Install Python interpreter under e.g. /snekbin/python/3.13/ (no patch version)
+# By dropping everything after, and including, the last period or hyphen.
+install_path="${py_version%[-.]*}"
+
+# If python version ends with a t, then ensure Python is installed to a dir ending with a t.
+if [[ $py_version == *t ]]; then
+    install_path+="t"
+fi
+
 "${PYENV_ROOT}/plugins/python-build/bin/python-build" \
     "${py_version}" \
-    "/snekbin/python/${py_version%[-.]*}"
-"/snekbin/python/${py_version%[-.]*}/bin/python" -m pip install -U pip
+    "/snekbin/python/${install_path}"
+"/snekbin/python/${install_path}/bin/python" -m pip install -U pip
 
 # Clean up some unnecessary files to reduce image size bloat.
 find /snekbin/python/ -depth \
diff --git a/tests/test_integration.py b/tests/test_integration.py
index 0d8f700d..ed44d86a 100644
--- a/tests/test_integration.py
+++ b/tests/test_integration.py
@@ -83,6 +83,26 @@ def test_alternate_executable_support(self):
                     self.assertEqual(status, 200)
                     self.assertEqual(json.loads(response)["stdout"], expected)
 
+    def test_gil_status(self):
+        """Test no-gil builds actually don't have a gil."""
+        with run_gunicorn():
+            get_gil_status = {
+                "input": "import sysconfig; print(sysconfig.get_config_var('Py_GIL_DISABLED'))"
+            }
+            cases = [
+                ("3.13", "0\n"),
+                ("3.13t", "1\n"),
+            ]
+            for version, expected in cases:
+                with self.subTest(version=version, expected=expected):
+                    payload = {
+                        "executable_path": f"/snekbin/python/{version}/bin/python",
+                        **get_gil_status,
+                    }
+                    response, status = snekbox_request(payload)
+                    self.assertEqual(status, 200)
+                    self.assertEqual(json.loads(response)["stdout"], expected)
+
     def invalid_executable_paths(self):
         """Test that passing invalid executable paths result in no code execution."""
         with run_gunicorn():