diff --git a/docs/news.rst b/docs/news.rst
index 31710fa3..fa942d98 100644
--- a/docs/news.rst
+++ b/docs/news.rst
@@ -1,6 +1,11 @@
 Release Notes
 =============
 
+**UNRELEASED**
+
+- Fixed ``wheel convert`` unnecessarily upgrading compatible core metadata versions
+  (`#643 <https://github.com/pypa/wheel/issues/643>`_)
+
 **0.47.0 (2026-04-22)**
 
 - Added the ``wheel info`` subcommand to display metadata about wheel files without
diff --git a/src/wheel/_commands/convert.py b/src/wheel/_commands/convert.py
index cafd12c8..567cb7d1 100644
--- a/src/wheel/_commands/convert.py
+++ b/src/wheel/_commands/convert.py
@@ -66,6 +66,7 @@ def convert_requires(requires: str, metadata: Message) -> None:
 
 def convert_pkg_info(pkginfo: str, metadata: Message) -> None:
     parsed_message = Parser().parsestr(pkginfo)
+    metadata_version = parsed_message.get("Metadata-Version", "1.0")
     for key, value in parsed_message.items():
         key_lower = key.lower()
         if value == "UNKNOWN":
@@ -92,7 +93,23 @@ def convert_pkg_info(pkginfo: str, metadata: Message) -> None:
         else:
             metadata.add_header(key, value)
 
-    metadata.replace_header("Metadata-Version", "2.4")
+    metadata.replace_header(
+        "Metadata-Version",
+        _compatible_metadata_version(metadata_version),
+    )
+
+
+def _compatible_metadata_version(metadata_version: str) -> str:
+    try:
+        major_str, minor_str = metadata_version.split(".", 1)
+        major_minor = (int(major_str), int(minor_str))
+    except ValueError:
+        return "1.2"
+
+    if major_minor < (1, 2):
+        return "1.2"
+
+    return metadata_version
 
 
 def normalize(name: str) -> str:
diff --git a/tests/commands/test_convert.py b/tests/commands/test_convert.py
index 73ed81ef..dcf1846c 100644
--- a/tests/commands/test_convert.py
+++ b/tests/commands/test_convert.py
@@ -42,7 +42,7 @@
 """
 
 EXPECTED_METADATA = """\
-Metadata-Version: 2.4
+Metadata-Version: 2.1
 Name: Sampledist
 Version: 1.0.0
 Author: Alex Grönholm
@@ -289,3 +289,15 @@ def test_convert_pkg_info_with_one_line_description() -> None:
     convert_pkg_info(pkginfo, message)
     assert message.get_all("Name") == ["Sampledist"]
     assert message.get_payload() == "My cool package\n\n\n"
+
+
+def test_convert_pkg_info_uses_lowest_compatible_metadata_version() -> None:
+    pkginfo = """\
+Metadata-Version: 1.1
+Name: Sampledist
+Version: 1.0.0
+Home-page: https://example.com
+"""
+    message = Message()
+    convert_pkg_info(pkginfo, message)
+    assert message["Metadata-Version"] == "1.2"