diff --git a/docs/conf.py b/docs/conf.py
index aae0304ac6..876f676881 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -53,10 +53,9 @@ sys.path.insert(0, os.path.join(qemu_docdir, "../scripts"))
 
 # If your documentation needs a minimal Sphinx version, state it here.
 #
-# Sphinx 1.5 and earlier can't build our docs because they are too
-# picky about the syntax of the argument to the option:: directive
-# (see Sphinx bugs #646, #3366).
-needs_sphinx = '1.6'
+# 3.4.3 is the oldest version of Sphinx that ships on a platform we
+# pledge build support for.
+needs_sphinx = '3.4.3'
 
 # Add any Sphinx extension module names here, as strings. They can be
 # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
diff --git a/pythondeps.toml b/pythondeps.toml
index 6aba0c9daa..f6e590fdd8 100644
--- a/pythondeps.toml
+++ b/pythondeps.toml
@@ -23,7 +23,7 @@ meson = { accepted = ">=1.1.0", installed = "1.2.3", canary = "meson" }
 
 [docs]
 # Please keep the installed versions in sync with docs/requirements.txt
-sphinx = { accepted = ">=1.6", installed = "5.3.0", canary = "sphinx-build" }
+sphinx = { accepted = ">=3.4.3", installed = "5.3.0", canary = "sphinx-build" }
 sphinx_rtd_theme = { accepted = ">=0.5", installed = "1.1.1" }
 
 [avocado]