diff --git a/spacy/spans.pxd b/spacy/spans.pxd
index 180a991ee..ffbac9c36 100644
--- a/spacy/spans.pxd
+++ b/spacy/spans.pxd
@@ -12,6 +12,3 @@ cdef class Span:
     cdef public int start
     cdef public int end
     cdef readonly int label
-    cdef public Span head
-    cdef public list rights
-    cdef public list lefts
diff --git a/spacy/spans.pyx b/spacy/spans.pyx
index 76f281b7c..50ccf2bfa 100644
--- a/spacy/spans.pyx
+++ b/spacy/spans.pyx
@@ -9,10 +9,6 @@ cdef class Span:
         self.start = start
         self.end = end
         self.label = label
-        self.head = self
-
-        self.rights = []
-        self.lefts = []
 
     def __richcmp__(self, Span other, int op):
         # Eq
@@ -41,6 +37,37 @@ cdef class Span:
         for i in range(self.start, self.end):
             yield self._seq[i]
 
+    property head:
+        """The highest Token in the dependency tree in the Span, or None if
+        the Span is not internally connected (i.e. there are multiple heads).
+        """
+        def __get__(self):
+            heads = []
+            for token in self:
+                head_i = token.head.i
+                if token.head is token or head_i >= self.end or head_i < self.start:
+                    heads.append(token)
+            if len(heads) != 1:
+                return None
+            else:
+                return heads[0]
+
+    property lefts:
+        """Tokens that are to the left of the Span, whose head is within the Span."""
+        def __get__(self):
+            for token in reversed(self): # Reverse, so we get the tokens in order
+                for left in token.lefts:
+                    if left.i < self.start:
+                        yield left
+
+    property right:
+        """Tokens that are to the right of the Span, whose head is within the Span."""
+        def __get__(self):
+            for token in self:
+                for right in token.rights:
+                    if right.i >= self.end:
+                        yield right
+
     property orth_:
         def __get__(self):
             return ''.join([t.string for t in self]).strip()