diff --git a/manimlib/mobject/functions.py b/manimlib/mobject/functions.py
index e67abeee..dafede7b 100644
--- a/manimlib/mobject/functions.py
+++ b/manimlib/mobject/functions.py
@@ -1,7 +1,6 @@
 from manimlib.constants import *
 from manimlib.mobject.types.vectorized_mobject import VMobject
 from manimlib.utils.config_ops import digest_config
-from manimlib.utils.space_ops import get_norm
 
 
 class ParametricCurve(VMobject):
@@ -11,7 +10,6 @@ class ParametricCurve(VMobject):
         "epsilon": 1e-8,
         # TODO, automatically figure out discontinuities
         "discontinuities": [],
-        "smoothing": True,
     }
 
     def __init__(self, t_func, t_range=None, **kwargs):
@@ -42,8 +40,7 @@ class ParametricCurve(VMobject):
             points = np.array([self.t_func(t) for t in t_range])
             self.start_new_path(points[0])
             self.add_points_as_corners(points[1:])
-        if self.smoothing:
-            self.make_smooth()
+        self.make_smooth(true_smooth=False)
         return self
 
 
diff --git a/manimlib/mobject/types/vectorized_mobject.py b/manimlib/mobject/types/vectorized_mobject.py
index a5d64413..905546ae 100644
--- a/manimlib/mobject/types/vectorized_mobject.py
+++ b/manimlib/mobject/types/vectorized_mobject.py
@@ -9,6 +9,7 @@ from manimlib.mobject.mobject import Mobject
 from manimlib.mobject.mobject import Point
 from manimlib.utils.bezier import bezier
 from manimlib.utils.bezier import get_smooth_quadratic_bezier_handle_points
+from manimlib.utils.bezier import get_smooth_cubic_bezier_handle_points
 from manimlib.utils.bezier import get_quadratic_approximation_of_cubic
 from manimlib.utils.bezier import interpolate
 from manimlib.utils.bezier import integer_interpolate
@@ -402,13 +403,13 @@ class VMobject(Mobject):
         ])
         return self
 
-    def set_points_smoothly(self, points):
+    def set_points_smoothly(self, points, true_smooth=False):
         self.set_points_as_corners(points)
-        self.make_smooth()
+        self.make_smooth(true_smooth)
         return self
 
     def change_anchor_mode(self, mode):
-        assert(mode in ["jagged", "smooth"])
+        assert(mode in ["jagged", "approx_smooth", "true_smooth"])
         nppc = self.n_points_per_curve
         for submob in self.family_members_with_points():
             subpaths = submob.get_subpaths()
@@ -416,17 +417,27 @@ class VMobject(Mobject):
             for subpath in subpaths:
                 anchors = np.vstack([subpath[::nppc], subpath[-1:]])
                 new_subpath = np.array(subpath)
-                if mode == "smooth":
+                if mode == "approx_smooth":
                     new_subpath[1::nppc] = get_smooth_quadratic_bezier_handle_points(anchors)
+                elif mode == "true_smooth":
+                    h1, h2 = get_smooth_cubic_bezier_handle_points(anchors)
+                    new_subpath = get_quadratic_approximation_of_cubic(anchors[:-1], h1, h2, anchors[1:])
                 elif mode == "jagged":
                     new_subpath[1::nppc] = 0.5 * (anchors[:-1] + anchors[1:])
                 submob.append_points(new_subpath)
             submob.refresh_triangulation()
         return self
 
-    def make_smooth(self):
-        # TODO, Change this to not rely on a cubic-to-quadratic conversion
-        return self.change_anchor_mode("smooth")
+    def make_smooth(self, true_smooth=True):
+        """
+        If true_smooth is set to True, the number of points
+        in the mobject will double, but the effect will be
+        a genuinely smooth (C2) curve.  Otherwise, it may not
+        becomes perfectly smooth, but the number of points
+        will stay the same.
+        """
+        mode = "true_smooth" if true_smooth else "approx_smooth"
+        return self.change_anchor_mode(mode)
 
     def make_jagged(self):
         return self.change_anchor_mode("jagged")
@@ -824,7 +835,7 @@ class VMobject(Mobject):
     def apply_function(self, function):
         super().apply_function(function)
         if self.make_smooth_after_applying_functions:
-            self.make_smooth()
+            self.make_smooth(true_smooth=False)
         return self
 
     @triggers_refreshed_triangulation
diff --git a/manimlib/utils/bezier.py b/manimlib/utils/bezier.py
index 23acc4ef..8a3f6692 100644
--- a/manimlib/utils/bezier.py
+++ b/manimlib/utils/bezier.py
@@ -134,8 +134,14 @@ def get_smooth_quadratic_bezier_handle_points(points):
         0.25 * ps[0:-2] + ps[1:-1] - 0.25 * ps[2:]
         for ps in (points, points[::-1])
     ]
-    handles = 0.5 * np.vstack([smooth_to_right, [smooth_to_left[0]]])
-    handles += 0.5 * np.vstack([smooth_to_right[0], smooth_to_left[::-1]])
+    if np.isclose(points[0], points[-1]).all():
+        last_str = 0.25 * points[-2] + points[-1] - 0.25 * points[1]
+        last_stl = 0.25 * points[1] + points[0] - 0.25 * points[-2]
+    else:
+        last_str = smooth_to_left[0]
+        last_stl = smooth_to_right[0]
+    handles = 0.5 * np.vstack([smooth_to_right, [last_str]])
+    handles += 0.5 * np.vstack([last_stl, smooth_to_left[::-1]])
     return handles