diff --git a/README.md b/README.md
index 26a647e..790b482 100644
--- a/README.md
+++ b/README.md
@@ -135,6 +135,20 @@ them into the constructor like so
 
 The last line (calling `__init__` on the super class) is critical.
 
+## Implementation Details
+
+The simulated annealing algorithm requires that we track states (current, previous, best), which means we need to copy `self.state` frequently.
+
+Copying an object in Python is not always straightforward or performant. The standard library provides a `copy.deepcopy()` method to copy arbitrary python objects but it is very expensive. Certain objects can be copied by more efficient means: lists can be sliced and dictionaries can use their own .copy method, etc.
+
+In order to facilitate flexibility, you can specify the `copy_strategy` attribute
+which defines one of:
+* `deepcopy`: uses `copy.deepcopy(object)`
+* `slice`: uses `object[:]`
+* `method`: uses `object.copy()`
+
+If you want to implement your own custom copy mechanism, override the `copy_state` method.
+
 ## Optimizations
 
 For some problems the `energy` function is prohibitively expensive to calculate
@@ -149,19 +163,12 @@ energy from the previous state, this approach will save you a call to
 value and sometimes return `None`, depending on the type of modification it
 makes to the state and the complexity of calculting a delta.
 
-## Implementation Details
-
-The simulated annealing algorithm requires that we track states (current, previous, best), which means we need to copy `self.state` frequently.
-
-Copying an object in Python is not always straightforward or performant. The standard library provides a `copy.deepcopy()` method to copy arbitrary python objects but it is very expensive. Certain objects can be copied by more efficient means: lists can be sliced and dictionaries can use their own .copy method, etc.
-
-In order to facilitate flexibility, you can specify the `copy_strategy` attribute
-which defines one of:
-* `deepcopy`: uses `copy.deepcopy(object)`
-* `slice`: uses `object[:]`
-* `method`: uses `object.copy()`
-
-If you want to implement your own custom copy mechanism, override the `copy_state` method.
+Another optimization relates to avoiding copying the state for every move; 
+for some problems it is possible to easily undo the last move. For
+such problems your class can implement an `undo_move(self)` method, which changes
+`self.state` back to the state it was in before the last `move(self)` method call. 
+Using this method almost all the copying can be avoided, which may significantly 
+speed up the annealing process if the copies themselves take a lot of time.
 
 ## Notes
 
diff --git a/simanneal/anneal.py b/simanneal/anneal.py
index 3b70d81..d40e07c 100644
--- a/simanneal/anneal.py
+++ b/simanneal/anneal.py
@@ -58,6 +58,8 @@ def __init__(self, initial_state=None, load_state=None):
             raise ValueError('No valid values supplied for neither \
             initial_state nor load_state')
 
+        self.supports_undo_move = hasattr(self, 'undo_move')
+
         signal.signal(signal.SIGINT, self.set_user_exit)
 
     def save_state(self, fname=None):
@@ -115,6 +117,15 @@ def copy_state(self, state):
                                'the self.copy_strategy "%s"' %
                                self.copy_strategy)
 
+    def restore_state(self, state):
+        """Restore the state to a provided state either by making a copy,
+        or by undoing the last move via self.undo_move method if it exists
+        """
+        if self.supports_undo_move:
+            self.undo_move()
+        else:
+            self.state = self.copy_state(state)
+
     def update(self, *args, **kwargs):
         """Wrapper for internal update.
 
@@ -188,7 +199,7 @@ def anneal(self):
         # Note initial state
         T = self.Tmax
         E = self.energy()
-        prevState = self.copy_state(self.state)
+        prevState = self.copy_state(self.state) if not self.supports_undo_move else None
         prevEnergy = E
         self.best_state = self.copy_state(self.state)
         self.best_energy = E
@@ -209,15 +220,14 @@ def anneal(self):
                 E += dE
             trials += 1
             if dE > 0.0 and math.exp(-dE / T) < random.random():
-                # Restore previous state
-                self.state = self.copy_state(prevState)
+                self.restore_state(prevState)
                 E = prevEnergy
             else:
                 # Accept new state and compare to best state
                 accepts += 1
                 if dE < 0.0:
                     improves += 1
-                prevState = self.copy_state(self.state)
+                prevState = self.copy_state(self.state) if not self.supports_undo_move else None
                 prevEnergy = E
                 if E < self.best_energy:
                     self.best_state = self.copy_state(self.state)
@@ -246,7 +256,7 @@ def run(T, steps):
             """Anneals a system at constant temperature and returns the state,
             energy, rate of acceptance, and rate of improvement."""
             E = self.energy()
-            prevState = self.copy_state(self.state)
+            prevState = self.copy_state(self.state) if not self.supports_undo_move else None
             prevEnergy = E
             accepts, improves = 0, 0
             for _ in range(steps):
@@ -257,13 +267,13 @@ def run(T, steps):
                 else:
                     E = prevEnergy + dE
                 if dE > 0.0 and math.exp(-dE / T) < random.random():
-                    self.state = self.copy_state(prevState)
+                    self.state = self.restore_state(prevState)
                     E = prevEnergy
                 else:
                     accepts += 1
                     if dE < 0.0:
                         improves += 1
-                    prevState = self.copy_state(self.state)
+                    prevState = self.copy_state(self.state) if not self.supports_undo_move else None
                     prevEnergy = E
             return E, float(accepts) / steps, float(improves) / steps