diff --git a/gio/gdbus-2.0/codegen/codegen_main.py b/gio/gdbus-2.0/codegen/codegen_main.py
index a9dfe0428..aecacc76d 100644
--- a/gio/gdbus-2.0/codegen/codegen_main.py
+++ b/gio/gdbus-2.0/codegen/codegen_main.py
@@ -256,12 +256,17 @@ def codegen_main():
     else:
         glib_min_version = (2, 30)
 
+    glib_min_version_is_2_64 = (glib_min_version[0] > 2 or
+                                (glib_min_version[0] == 2 and
+                                 glib_min_version[1] >= 64))
+
     all_ifaces = []
     input_files_basenames = []
     for fname in sorted(args.files + args.xml_files):
         with open(fname, 'rb') as f:
             xml_data = f.read()
-        parsed_ifaces = parser.parse_dbus_xml(xml_data)
+        parsed_ifaces = parser.parse_dbus_xml(xml_data,
+                                              h_type_implies_unix_fd=glib_min_version_is_2_64)
         all_ifaces.extend(parsed_ifaces)
         input_files_basenames.append(os.path.basename(fname))
 
diff --git a/gio/gdbus-2.0/codegen/dbustypes.py b/gio/gdbus-2.0/codegen/dbustypes.py
index 16364f9b7..415a5cc7a 100644
--- a/gio/gdbus-2.0/codegen/dbustypes.py
+++ b/gio/gdbus-2.0/codegen/dbustypes.py
@@ -252,8 +252,9 @@ class Arg:
             a.post_process(interface_prefix, cns, cns_upper, cns_lower, self)
 
 class Method:
-    def __init__(self, name):
+    def __init__(self, name, h_type_implies_unix_fd=True):
         self.name = name
+        self.h_type_implies_unix_fd = h_type_implies_unix_fd
         self.in_args = []
         self.out_args = []
         self.annotations = []
@@ -284,10 +285,14 @@ class Method:
         for a in self.in_args:
             a.post_process(interface_prefix, cns, cns_upper, cns_lower, arg_count)
             arg_count += 1
+            if self.h_type_implies_unix_fd and 'h' in a.signature:
+                self.unix_fd = True
 
         for a in self.out_args:
             a.post_process(interface_prefix, cns, cns_upper, cns_lower, arg_count)
             arg_count += 1
+            if self.h_type_implies_unix_fd and 'h' in a.signature:
+                self.unix_fd = True
 
         if utils.lookup_annotation(self.annotations, 'org.freedesktop.DBus.Deprecated') == 'true':
             self.deprecated = True
diff --git a/gio/gdbus-2.0/codegen/parser.py b/gio/gdbus-2.0/codegen/parser.py
index f49136d6e..7dcc73558 100644
--- a/gio/gdbus-2.0/codegen/parser.py
+++ b/gio/gdbus-2.0/codegen/parser.py
@@ -36,7 +36,7 @@ class DBusXMLParser:
     STATE_ANNOTATION = 'annotation'
     STATE_IGNORED = 'ignored'
 
-    def __init__(self, xml_data):
+    def __init__(self, xml_data, h_type_implies_unix_fd=True):
         self._parser = xml.parsers.expat.ParserCreate()
         self._parser.CommentHandler = self.handle_comment
         self._parser.CharacterDataHandler = self.handle_char_data
@@ -53,6 +53,8 @@ class DBusXMLParser:
 
         self.doc_comment_last_symbol = ''
 
+        self._h_type_implies_unix_fd = h_type_implies_unix_fd
+
         self._parser.Parse(xml_data)
 
     COMMENT_STATE_BEGIN = 'begin'
@@ -163,7 +165,8 @@ class DBusXMLParser:
         elif self.state == DBusXMLParser.STATE_INTERFACE:
             if name == DBusXMLParser.STATE_METHOD:
                 self.state = DBusXMLParser.STATE_METHOD
-                method = dbustypes.Method(attrs['name'])
+                method = dbustypes.Method(attrs['name'],
+                                          h_type_implies_unix_fd=self._h_type_implies_unix_fd)
                 self._cur_object.methods.append(method)
                 self._cur_object = method
             elif name == DBusXMLParser.STATE_SIGNAL:
@@ -288,6 +291,6 @@ class DBusXMLParser:
         self.state = self.state_stack.pop()
         self._cur_object = self._cur_object_stack.pop()
 
-def parse_dbus_xml(xml_data):
-    parser = DBusXMLParser(xml_data)
+def parse_dbus_xml(xml_data, h_type_implies_unix_fd):
+    parser = DBusXMLParser(xml_data, h_type_implies_unix_fd)
     return parser.parsed_interfaces
diff --git a/gio/tests/codegen.py b/gio/tests/codegen.py
index 6a01b2f00..dc2c9ff1a 100644
--- a/gio/tests/codegen.py
+++ b/gio/tests/codegen.py
@@ -397,6 +397,56 @@ G_END_DECLS
         self.assertEqual('', result.err)
         self.assertNotEqual('', result.out.strip())
 
+    def test_unix_fd_types_and_annotations(self):
+        """Test an interface with `h` arguments, no annotation, and GLib < 2.64.
+
+        See issue #1726.
+        """
+        interface_xml = '''
+            <node>
+              <interface name="FDPassing">
+                <method name="HelloFD">
+                  <annotation name="org.gtk.GDBus.C.UnixFD" value="1"/>
+                  <arg name="greeting" direction="in" type="s"/>
+                  <arg name="response" direction="out" type="s"/>
+                </method>
+                <method name="NoAnnotation">
+                  <arg name="greeting" direction="in" type="h"/>
+                  <arg name="greeting_locale" direction="in" type="s"/>
+                  <arg name="response" direction="out" type="h"/>
+                  <arg name="response_locale" direction="out" type="s"/>
+                </method>
+                <method name="NoAnnotationNested">
+                  <arg name="files" type="a{sh}" direction="in"/>
+                </method>
+              </interface>
+            </node>'''
+
+        # Try without specifying --glib-min-version.
+        result = self.runCodegenWithInterface(interface_xml,
+                                              '--output', '/dev/stdout',
+                                              '--header')
+        self.assertEqual('', result.err)
+        self.assertEqual(result.out.strip().count('GUnixFDList'), 6)
+
+        # Specify an old --glib-min-version.
+        result = self.runCodegenWithInterface(interface_xml,
+                                              '--output', '/dev/stdout',
+                                              '--header',
+                                              '--glib-min-version', '2.32')
+        self.assertEqual('', result.err)
+        self.assertEqual(result.out.strip().count('GUnixFDList'), 6)
+
+        # Specify a --glib-min-version ≥ 2.64. There should be more
+        # mentions of `GUnixFDList` now, since the annotation is not needed to
+        # trigger its use.
+        result = self.runCodegenWithInterface(interface_xml,
+                                              '--output', '/dev/stdout',
+                                              '--header',
+                                              '--glib-min-version', '2.64')
+        self.assertEqual('', result.err)
+        self.assertEqual(result.out.strip().count('GUnixFDList'), 18)
+
 
 if __name__ == '__main__':
     unittest.main(testRunner=taptestrunner.TAPTestRunner())