diff --git a/src/emeraldtree/ElementPath.py b/src/emeraldtree/ElementPath.py
index 55b9952..8392ebb 100644
--- a/src/emeraldtree/ElementPath.py
+++ b/src/emeraldtree/ElementPath.py
@@ -102,15 +102,22 @@ 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 = {}
-            for p in context.root.iter():
-                for e in p:
-                    parent_map[e] = p
         for elem in result:
-            if elem in parent_map:
-                yield parent_map[elem]
+            parent = getattr(elem, '_parent', None)
+            if parent is not None:
+                yield parent
+            else:
+                if context.parent_map is None:
+                    context.parent_map = {}
+                    for p in context.root.iter():
+                        try:
+                            iter(p)
+                        except TypeError:
+                            continue
+                        for e in p:
+                            context.parent_map[e] = p
+                if elem in context.parent_map:
+                    yield context.parent_map[elem]
     return select
 
 def prepare_predicate(next, token):
@@ -146,10 +153,21 @@ def select(context, result):
         token = next()
         if token[0] != "]":
             raise SyntaxError("invalid node predicate")
-        def select(context, result):
-            for elem in result:
-                if elem.find(tag) is not None:
-                    yield elem
+        try:
+            index = int(tag)
+        except ValueError:
+            def select(context, result):
+                for elem in result:
+                    if elem.find(tag) is not None:
+                        yield elem
+        else:
+            if index < 1:
+                raise SyntaxError("XPath position >= 1 expected")
+            def select(context, result):
+                for i, elem in enumerate(result):
+                    if i + 1 == index:
+                        yield elem
+                        break
     else:
         raise SyntaxError("invalid predicate")
     return select
diff --git a/src/emeraldtree/tests/test_tree.py b/src/emeraldtree/tests/test_tree.py
index 5aff12e..7758d48 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"
@@ -235,7 +232,6 @@ def test_Element_findall_attribute():
     assert len(result) == 0
 
 def test_Element_findall_position():
-    pytest.skip('not supported')
     c1 = Element('c')
     c2 = Element('c')
     text = "text"
@@ -251,6 +247,13 @@ def test_Element_findall_position():
     assert len(result) == 1
     assert result[0] is c2
 
+def test_Element_findall_position_invalid():
+    b1 = Element('b')
+    with pytest.raises(SyntaxError):
+        list(b1.findall('c[0]'))
+    with pytest.raises(SyntaxError):
+        list(b1.findall('c[-1]'))
+
 def test_Element_findtext_default():
     elem = Element('a')
     default_text = 'defaulttext'
diff --git a/src/emeraldtree/tree.py b/src/emeraldtree/tree.py
index b2ebff7..2ac9faa 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