diff --git a/CHANGELOG.md b/CHANGELOG.md
index 117e17ba..4ee707a1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,14 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/)
 and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.html).
 
 <!-- insertion marker -->
+## [1.6.2](https://github.com/mkdocstrings/python/releases/tag/1.6.2) - 2023-09-05
+
+<small>[Compare with 1.6.1](https://github.com/mkdocstrings/python/compare/1.6.1...1.6.2)</small>
+
+### Bug Fixes
+
+- Don't render cross-ref spans when they're not enabled ([eed51ee](https://github.com/mkdocstrings/python/commit/eed51ee14bd973a08395f95377f9bd4cd38febfc) by Timothée Mazzucotelli).
+
 ## [1.6.1](https://github.com/mkdocstrings/python/releases/tag/1.6.1) - 2023-09-04
 
 <small>[Compare with 1.6.0](https://github.com/mkdocstrings/python/compare/1.6.0...1.6.1)</small>
diff --git a/src/mkdocstrings_handlers/python/rendering.py b/src/mkdocstrings_handlers/python/rendering.py
index b2869bf9..46b34c01 100644
--- a/src/mkdocstrings_handlers/python/rendering.py
+++ b/src/mkdocstrings_handlers/python/rendering.py
@@ -88,13 +88,17 @@ def do_format_signature(
     function: Function,
     line_length: int,
     *,
+    annotations: bool | None = None,  # noqa: ARG001
     crossrefs: bool = False,  # noqa: ARG001
 ) -> str:
     """Format a signature using Black.
 
     Parameters:
+        context: Jinja context, passed automatically.
         callable_path: The path of the callable we render the signature of.
+        function: The function we render the signature of.
         line_length: The line length to give to Black.
+        annotations: Whether to show type annotations.
         crossrefs: Whether to cross-reference types in the signature.
 
     Returns:
@@ -126,6 +130,7 @@ def do_format_attribute(
     """Format an attribute using Black.
 
     Parameters:
+        context: Jinja context, passed automatically.
         attribute_path: The path of the callable we render the signature of.
         attribute: The attribute we render the signature of.
         line_length: The line length to give to Black.
diff --git a/src/mkdocstrings_handlers/python/templates/material/_base/expression.html b/src/mkdocstrings_handlers/python/templates/material/_base/expression.html
index 52d3a624..6ba78963 100644
--- a/src/mkdocstrings_handlers/python/templates/material/_base/expression.html
+++ b/src/mkdocstrings_handlers/python/templates/material/_base/expression.html
@@ -8,9 +8,13 @@
       {%- set annotation = full -%}
     {%- endif -%}
     {%- for title, path in annotation|split_path(full) -%}
-      {%- filter stash_crossref(length=title|length) -%}
-        <span data-autorefs-optional{% if title != path %}-hover{% endif %}="{{ path }}">{{ title }}</span>
-      {%- endfilter -%}
+      {%- if not signature or config.signature_crossrefs -%}
+        {%- filter stash_crossref(length=title|length) -%}
+          <span data-autorefs-optional{% if title != path %}-hover{% endif %}="{{ path }}">{{ title }}</span>
+        {%- endfilter -%}
+      {%- else -%}
+        {{ title }}
+      {%- endif -%}
       {%- if not loop.last -%}.{%- endif -%}
     {%- endfor -%}
   {%- endwith -%}