diff --git a/clusterview/points.py b/clusterview/points.py
index 3d19d50..88b0de5 100644
--- a/clusterview/points.py
+++ b/clusterview/points.py
@@ -71,7 +71,7 @@ class Point:
                                   self.__y + half_point)
 
         self.__bottom_right_corner = (self.__x + half_point,
-                                  self.__y - half_point)
+                                      self.__y - half_point)
 
     def __check_window_bounds(self, x, y):
         """
@@ -122,13 +122,6 @@ class Point:
                 self.__y == other.y and
                 self.__point_size == other.point_size)
 
-    def __hash__(self):
-        """
-        Overridden hashing function so it can be used as a dictionary key
-        for attributes.
-        """
-        return hash((self.__x, self.__y, self.__point_size))
-
     def __repr__(self):
 
         # For some reason I had to split this instead of using one giant
@@ -192,8 +185,10 @@ class Attribute:
 
 class PointSet:
     """
-    Useful container for points backed by a set to insure point
-    uniqueness.
+    Useful container for points. Since points are not hashable (they are
+    modified in place by move) we are forced to back the PointSet with an
+    array. However, it is still a "set" in the "uniqueness among all points"
+    sense because `add_point` will reject a point with a duplicate center.
     """
 
     def __init__(self, point_size, viewport_width, viewport_height):
@@ -206,7 +201,7 @@ class PointSet:
         @param viewport_height The height of the viewport for bounds
                calculations.
         """
-        self.__points = set()
+        self.__points = []
         self.__point_size = point_size
         self.__viewport_width = viewport_width
         self.__viewport_height = viewport_height
@@ -218,7 +213,7 @@ class PointSet:
 
         attributes_equal = True
 
-        other_points = set(other.points)
+        other_points = list(other.points)
 
         attributes_equal = (attributes_equal and
                            (len(self.__points) == len(other_points)))
@@ -316,12 +311,16 @@ class PointSet:
         for attr in attrs:
             point.add_attribute(attr)
 
-        self.__points.add(point)
+        if point in self.__points:
+            # Silently reject a duplicate point (same center).
+            return
+
+        self.__points.append(point)
 
     def remove_point(self, x, y):
         """
-        Removes a point and it's attributes from the point set based
-        on a bounding box calculation.
+        Removes a point from the point set based on a bounding
+        box calculation.
 
         Removing a point is an exercise is determining which points
         have been hit, and then pulling them out of the list.
@@ -334,9 +333,6 @@ class PointSet:
         @param x The x-coordinate.
         @param y The y-coordinate.
         """
-
-        # Find points that match
-        matched = set(p for p in self.__points if p.hit(x, y))
-
-        # In place set difference
-        self.__points = self.__points - matched
+        for p in self.__points:
+            if p.hit(x, y):
+                self.__points.remove(p)