diff --git a/internal/phpast/docparam_test.go b/internal/phpast/docparam_test.go
index 533748db..65607a75 100644
--- a/internal/phpast/docparam_test.go
+++ b/internal/phpast/docparam_test.go
@@ -26,6 +26,18 @@ func TestStripRedundantDocParams(t *testing.T) {
 			added: map[string]string{"d": "\\DateTime"},
 			want:  "<?php\nclass A {\n    public function m($d) {}\n}",
 		},
+		{
+			name:  "matches a union regardless of member order",
+			src:   "<?php\nclass A {\n    /**\n     * @param string|array $c\n     */\n    public function m($c) {}\n}",
+			added: map[string]string{"c": "array|string"},
+			want:  "<?php\nclass A {\n    public function m($c) {}\n}",
+		},
+		{
+			name:  "matches an imported short name against a fully qualified union member",
+			src:   "<?php\nclass A {\n    /**\n     * @param CompositeExpression|string $e\n     */\n    public function m($e) {}\n}",
+			added: map[string]string{"e": "\\Doctrine\\DBAL\\Query\\Expression\\CompositeExpression|string"},
+			want:  "<?php\nclass A {\n    public function m($e) {}\n}",
+		},
 		{
 			name:  "keeps a tag whose type differs from the added type",
 			src:   "<?php\nclass A {\n    /**\n     * @param mixed $v\n     */\n    public function m($v) {}\n}",
diff --git a/internal/phpast/phpast.go b/internal/phpast/phpast.go
index 867f8f74..993ca18b 100644
--- a/internal/phpast/phpast.go
+++ b/internal/phpast/phpast.go
@@ -6,6 +6,7 @@ import (
 	"bytes"
 	"reflect"
 	"regexp"
+	"slices"
 	"strings"
 
 	"github.com/rectorphp/php-parser-in-go/pkg/ast"
@@ -214,8 +215,20 @@ func docIsEmpty(lines []string) bool {
 	return true
 }
 
+// normalizeDocType reduces a type to a form that compares equal regardless of
+// union member order and of whether a class is written as a short name or a
+// fully qualified one: each member is cut to its last name part and the members
+// are sorted.
 func normalizeDocType(name string) string {
-	return strings.TrimPrefix(name, "\\")
+	parts := strings.Split(name, "|")
+	for i, part := range parts {
+		if index := strings.LastIndex(part, "\\"); index >= 0 {
+			part = part[index+1:]
+		}
+		parts[i] = part
+	}
+	slices.Sort(parts)
+	return strings.Join(parts, "|")
 }
 
 // leadingToken returns the first token of a function or method, which carries