diff --git a/pdfminer/layout.py b/pdfminer/layout.py
index a9237a8..6b8e911 100644
--- a/pdfminer/layout.py
+++ b/pdfminer/layout.py
@@ -546,11 +546,11 @@ class LTLayoutContainer(LTContainer):
             """
             return ((x1-x0)*(y1-y0) - obj1.width*obj1.height - obj2.width*obj2.height)
         boxes = boxes[:]
+        plane = Plane(boxes)
         # XXX this is very slow when there're many textboxes.
         while 2 <= len(boxes):
             mindist = (INF,0)
             minpair = None
-            plane = Plane(boxes)
             boxes = csort(boxes, key=lambda obj: obj.width*obj.height)
             for i in xrange(len(boxes)):
                 for j in xrange(i+1, len(boxes)):
@@ -571,6 +571,8 @@ class LTLayoutContainer(LTContainer):
             (obj1, obj2) = minpair
             boxes.remove(obj1)
             boxes.remove(obj2)
+            plane.remove(obj1)
+            plane.remove(obj2)
             if (isinstance(obj1, LTTextBoxVertical) or
                 isinstance(obj2, LTTextBoxVertical) or 
                 isinstance(obj1, LTTextGroupTBRL) or
@@ -578,7 +580,9 @@ class LTLayoutContainer(LTContainer):
                 group = LTTextGroupTBRL([obj1, obj2])
             else:
                 group = LTTextGroupLRTB([obj1, obj2])
-            boxes.append(group.analyze(laparams))
+            group.analyze(laparams)
+            boxes.append(group)
+            plane.add(group)
         assert len(boxes) == 1
         return boxes.pop()
     
diff --git a/pdfminer/utils.py b/pdfminer/utils.py
index d3d0b76..0d531c3 100644
--- a/pdfminer/utils.py
+++ b/pdfminer/utils.py
@@ -220,7 +220,7 @@ class Plane(object):
                 yield (x,y)
         return
     
-    # add(obj): place an object in a certain area.
+    # add(obj): place an object.
     def add(self, obj):
         for k in self._getrange((obj.x0, obj.y0, obj.x1, obj.y1)):
             if k not in self._objs:
@@ -231,6 +231,15 @@ class Plane(object):
             r.append(obj)
         return
 
+    # remove(obj): displace an object.
+    def remove(self, obj):
+        for k in self._getrange((obj.x0, obj.y0, obj.x1, obj.y1)):
+            try:
+                self._objs[k].remove(obj)
+            except (KeyError, ValueError):
+                pass
+        return
+
     # find(): finds objects that are in a certain area.
     def find(self, (x0,y0,x1,y1)):
         r = set()