diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 12fe688..2832af5 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -23,6 +23,8 @@ jobs:
               python-version: '3.11'
             - os: ubuntu-latest
               python-version: '3.12'
+            - os: ubuntu-latest
+              python-version: '3.13'
 
     runs-on: ${{ matrix.os }}
     timeout-minutes: 10
diff --git a/pyproject.toml b/pyproject.toml
index e20114c..355cdcc 100755
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -16,6 +16,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
     "License :: OSI Approved :: Python Software Foundation License",
     "Intended Audience :: Developers",
     "Topic :: Text Processing :: Markup :: HTML",
@@ -37,11 +38,11 @@ build-backend = "setuptools.build_meta"
 write_to = "src/emeraldtree/_version.py"
 
 [tool.tox]
-legacy_tox_ini = """
-[tox]
-envlist = py{39,310,311,312}
+requires = ["tox>=4"]
+env_list = ["py39", "py310", "py311", "py312", "py313"]
 
-[testenv]
-deps = pytest
-commands = pytest -rs --pyargs {posargs:emeraldtree}
-"""
+[tool.tox.env.py]
+deps = ["pytest"]
+commands = [
+    ["pytest", "-rs", "--pyargs", "{posargs:emeraldtree}"]
+]
diff --git a/src/emeraldtree/ElementPath.py b/src/emeraldtree/ElementPath.py
index 55b9952..3706df2 100644
--- a/src/emeraldtree/ElementPath.py
+++ b/src/emeraldtree/ElementPath.py
@@ -102,15 +102,30 @@ def select(context, result):
 
 def prepare_dot_dot(next, token):
     def select(context, result):
-        parent_map = context.parent_map
-        if parent_map is None:
-            context.parent_map = parent_map = {}
+        # Prefer direct parent pointer if available. This allows '..' from any node.
+        for elem in result:
+            parent = getattr(elem, '_parent', None)
+            if parent is not None:
+                yield parent
+        # Fallback: if no direct parents were found (e.g., foreign objects), try building a local parent map
+        # from the current context root, but only once.
+        # Note: This fallback cannot find parents outside the context subtree.
+        if context.parent_map is None:
+            parent_map = {}
+            # Build mapping only for Element children to avoid iterating over strings
             for p in context.root.iter():
+                # only consider Elements as parents
+                try:
+                    iterator = iter(p)
+                except TypeError:
+                    continue
                 for e in p:
                     parent_map[e] = p
+            context.parent_map = parent_map
+        # Yield parents for any remaining items not covered above
         for elem in result:
-            if elem in parent_map:
-                yield parent_map[elem]
+            if elem in context.parent_map:
+                yield context.parent_map[elem]
     return select
 
 def prepare_predicate(next, token):
diff --git a/src/emeraldtree/html.py b/src/emeraldtree/html.py
index 2d94742..21dd91e 100644
--- a/src/emeraldtree/html.py
+++ b/src/emeraldtree/html.py
@@ -93,9 +93,10 @@ def handle_starttag(self, tag, attrs):
                 elif k == "content":
                     content = v
             if http_equiv == "content-type" and content:
-                import cgi
-                _, params = cgi.parse_header(content)
-                encoding = params.get('charset')
+                from email.message import Message
+                msg = Message()
+                msg['content-type'] = content
+                encoding = msg.get_param('charset', header='content-type')
                 if encoding:
                     self.encoding = encoding
         if tag.name in self.AUTOCLOSE:
diff --git a/src/emeraldtree/tests/test_tree.py b/src/emeraldtree/tests/test_tree.py
index 5aff12e..01d436e 100644
--- a/src/emeraldtree/tests/test_tree.py
+++ b/src/emeraldtree/tests/test_tree.py
@@ -170,7 +170,6 @@ def test_Element_findall_bracketed_tag():
     assert result[0] is b1 # b1 has 'c' childs
 
 def test_Element_findall_dotdot():
-    pytest.skip('broken')
     c1 = Element('c')
     c2 = Element('c')
     text = "text"
@@ -184,7 +183,6 @@ def test_Element_findall_dotdot():
     assert result[1] is c2
 
 def test_Element_findall_slashslash():
-    pytest.skip('broken')
     c1 = Element('c')
     c2 = Element('c')
     text = "text"
@@ -199,7 +197,6 @@ def test_Element_findall_slashslash():
     assert result[1] is c2
 
 def test_Element_findall_dotslashslash():
-    pytest.skip('broken')
     c1 = Element('c')
     c2 = Element('c')
     text = "text"
diff --git a/src/emeraldtree/tree.py b/src/emeraldtree/tree.py
index 817566b..405bc64 100644
--- a/src/emeraldtree/tree.py
+++ b/src/emeraldtree/tree.py
@@ -121,6 +121,9 @@ class Element(Node):
 
     attrib = None
 
+    # Parent pointer (internal). None for root or detached elements.
+    _parent = None
+
     ##
     # (Attribute) Text before first subelement.  This is either a
     # string or the value None, if there was no text.
@@ -151,6 +154,10 @@ def __init__(self, tag, attrib=None, children=(), **extra):
         self.tag = tag
         self.attrib = attrib
         self._children = list(children)
+        # set parent pointers for element children
+        for ch in self._children:
+            if isinstance(ch, Element):
+                ch._parent = self
 
     def __repr__(self):
         return "<Element {} at {:x}>".format(repr(self.tag), id(self))
@@ -186,7 +193,34 @@ def __getitem__(self, index):
     # @exception AssertionError If element is not a valid object.
 
     def __setitem__(self, index, element):
-        self._children.__setitem__(index, element)
+        # clear parent of replaced children and set parent of new ones
+        if isinstance(index, slice):
+            # clear parents for removed elements
+            old_items = self._children[index]
+            for old in old_items:
+                if isinstance(old, Element):
+                    old._parent = None
+            # assign
+            self._children[index] = element
+            # set parents for new elements
+            try:
+                iterator = iter(element)
+            except TypeError:
+                iterator = None
+            if iterator is not None:
+                for new in element:
+                    if isinstance(new, Element):
+                        new._parent = self
+        else:
+            try:
+                old = self._children[index]
+            except Exception:
+                old = None
+            if isinstance(old, Element):
+                old._parent = None
+            self._children[index] = element
+            if isinstance(element, Element):
+                element._parent = self
 
     ##
     # Deletes the given subelement.
@@ -195,6 +229,19 @@ def __setitem__(self, index, element):
     # @exception IndexError If the given element does not exist.
 
     def __delitem__(self, index):
+        # clear parent pointer for removed element(s)
+        if isinstance(index, slice):
+            old_items = self._children[index]
+            for old in old_items:
+                if isinstance(old, Element):
+                    old._parent = None
+        else:
+            try:
+                old = self._children[index]
+            except Exception:
+                old = None
+            if isinstance(old, Element):
+                old._parent = None
         self._children.__delitem__(index)
 
     ##
@@ -205,6 +252,8 @@ def __delitem__(self, index):
 
     def append(self, element):
         self._children.append(element)
+        if isinstance(element, Element):
+            element._parent = self
 
     ##
     # Appends subelements from a sequence.
@@ -215,6 +264,9 @@ def append(self, element):
 
     def extend(self, elements):
         self._children.extend(elements)
+        for e in elements:
+            if isinstance(e, Element):
+                e._parent = self
 
     ##
     # Inserts a subelement at the given position in this element.
@@ -224,6 +276,8 @@ def extend(self, elements):
 
     def insert(self, index, element):
         self._children.insert(index, element)
+        if isinstance(element, Element):
+            element._parent = self
 
     ##
     # Removes a matching subelement.  Unlike the <b>find</b> methods,
@@ -236,11 +290,16 @@ def insert(self, index, element):
 
     def remove(self, element):
         self._children.remove(element)
+        if isinstance(element, Element):
+            element._parent = None
 
     ##
     # Removes all subelements.
 
     def remove_all(self):
+        for ch in self._children:
+            if isinstance(ch, Element):
+                ch._parent = None
         self._children = []
 
     ##
@@ -355,7 +414,8 @@ def iter(self, tag=None):
                 for e in e.iter(tag):
                     yield e
             else:
-                yield e
+                if tag is None:
+                    yield e
 
     ##
     # Creates a text iterator.  The iterator loops over this element