diff --git a/sphinx_better_subsection.py b/sphinx_better_subsection.py
index fb95267..f95d06f 100644
--- a/sphinx_better_subsection.py
+++ b/sphinx_better_subsection.py
@@ -34,10 +34,10 @@ class PreferSectionTarget(Transform):
     .. code-block:: xml
 
         ...
-            <target refid="a">
-            <target refid="b">
-            <target refid="c">
-            <section ids="section-title a b c">
+            <target ids="['a']" names="['a']">
+            <target ids="['b']" names="['b']">
+            <target ids="['c']" names="['c']">
+            <section ids="section-title" names="Section\\ Title">
                 ...
 
     Transforming it gives:
@@ -45,19 +45,19 @@ class PreferSectionTarget(Transform):
     .. code-block:: xml
 
         ...
-            <target refid="a">
-            <target refid="b">
+            <target ids="['a']" names="['a']">
+            <target ids="['b']" names="['b']">
             <target refid="c">
-            <section ids="c section-title a b">
+            <section ids="c section-title" names="c Section\\ Title">
                 ...
 
     Note that the other IDs are all preserved; only the order is modified.
     Nested subsections are also checked.
 
     """
-    # Post processing priority from
-    # https://www.sphinx-doc.org/en/master/extdev/appapi.html?highlight=transform#sphinx.application.Sphinx.add_transform
-    default_priority = 700
+    # Run before `docutils.transforms.references.PropagateTransform` which has
+    # priority 260.
+    default_priority = 255
 
     def apply(self):
         """Docutils transform entry point"""
@@ -79,14 +79,55 @@ def apply(self):
             # Filter away nodes that aren't targets
             if not isinstance(last, nodes.target):
                 continue
-            # Internal hyperlink targets have refid (external ones have refuri)
-            if "refid" not in last:
+            # Filter away targets with content
+            if (
+                isinstance(last.parent, nodes.TextElement)
+                or last.hasattr("refid")
+                or last.hasattr("refuri")
+                or last.hasattr("refname")
+            ):
                 continue
-            refid = last["refid"]
-            assert refid in node["ids"]
+
+            # Store ID and name
+            print(last.parent, node)
+            refname = last["names"][0]
+            refid = last["ids"][0]
+
+            # Propagate the previous target
+            # Source from `PropagateTargets.apply`
+            node["ids"].extend(last["ids"])
+            node["names"].extend(last["names"])
+            # Set defaults for node.expect_referenced_by_name/id.
+            if not hasattr(node, "expect_referenced_by_name"):
+                node.expect_referenced_by_name = {}
+            if not hasattr(node, "expect_referenced_by_id"):
+                node.expect_referenced_by_id = {}
+            for id_ in last["ids"]:
+                node.expect_referenced_by_id[id_] = last
+                # Update IDs to node mapping.
+                self.document.ids[id_] = node
+            last["ids"] = []
+            for name in last["names"]:
+                node.expect_referenced_by_name[name] = last
+            last["names"] = []
+            # If there are any expect_referenced_by_name/id attributes in
+            # target set, copy them to node.
+            node.expect_referenced_by_name.update(
+                getattr(last, "expect_referenced_by_name", {}))
+            node.expect_referenced_by_id.update(
+                getattr(last, "expect_referenced_by_id", {}))
+            # Set refid to point to the first former ID of target which is now
+            # an ID of next_node.
+            last["refid"] = refid
+            self.document.note_refid(last)
+            # End source
+
             # Prefer the target's ID
             node["ids"].remove(refid)
             node["ids"].insert(0, refid)
+            # Also prefer the target's name
+            node["names"].remove(refname)
+            node["names"].insert(0, refname)
 
 def setup(app):
     """Sphinx extension entry point"""