diff --git a/build_docs.py b/build_docs.py
index f76cf1a..251a1ec 100755
--- a/build_docs.py
+++ b/build_docs.py
@@ -804,30 +804,43 @@ def build(self) -> None:
     def build_venv(self) -> None:
         """Build a venv for the specific Python version.
 
-        So we can reuse them from builds to builds, while they contain
-        different Sphinx versions.
+        The venv is recreated from scratch for every build: pip considers
+        a requirement satisfied when the installed version number matches,
+        even if the requirement is a direct URL now pointing at different
+        code, so a reused venv can silently keep outdated packages
+        (see python/cpython#153227).
         """
         requirements = list(self.build_meta.dependencies)
         if self.includes_html:
             # opengraph previews
             requirements.append("matplotlib>=3")
 
-        venv_path = self.build_root / self.build_meta.venv_name
-        venv.create(venv_path, symlinks=os.name != "nt", with_pip=True)
+        venv_name = self.build_meta.venv_name
+        if self.select_output is not None:
+            # Never share a venv with a concurrent differently-selected
+            # build, which may recreate it mid-build.
+            venv_name += f"-{self.select_output}"
+        venv_path = self.build_root / venv_name
+        venv.create(
+            venv_path,
+            symlinks=os.name != "nt",
+            with_pip=True,
+            clear=True,
+            upgrade_deps=True,
+        )
+        python = venv_path / "bin" / "python"
+
+        if (self.checkout / "Doc" / "pylock.toml").exists():
+            requirements.remove("-rrequirements.txt")
+            run(
+                (python, "-m", "pip", "install", "-rpylock.toml"),
+                cwd=self.checkout / "Doc",
+            )
         run(
-            (
-                venv_path / "bin" / "python",
-                "-m",
-                "pip",
-                "install",
-                "--upgrade",
-                "--upgrade-strategy=eager",
-                self.theme,
-                *requirements,
-            ),
+            (python, "-m", "pip", "install", self.theme, *requirements),
             cwd=self.checkout / "Doc",
         )
-        run((venv_path / "bin" / "python", "-m", "pip", "freeze", "--all"))
+        run((python, "-m", "pip", "freeze", "--all"))
         self.venv = venv_path
 
     def setup_indexsidebar(self) -> None: