diff --git a/framework/include/base/DisplacedProblem.h b/framework/include/base/DisplacedProblem.h
index 9f0947ae93cd..d158d073e43e 100644
--- a/framework/include/base/DisplacedProblem.h
+++ b/framework/include/base/DisplacedProblem.h
@@ -174,6 +174,12 @@ class DisplacedProblem : public SubProblem
    */
   virtual void registerRestartableData(std::string name, RestartableDataValue * data, THREAD_ID tid);
 
+  /**
+   * Resets the displaced mesh to the reference mesh.  Required when
+   * refining the DisplacedMesh.
+   */
+  void undisplaceMesh();
+
 protected:
   FEProblem & _mproblem;
   MooseMesh & _mesh;
diff --git a/framework/include/base/UpdateDisplacedMeshThread.h b/framework/include/base/UpdateDisplacedMeshThread.h
index d3d56e21387f..f945bb6fa096 100644
--- a/framework/include/base/UpdateDisplacedMeshThread.h
+++ b/framework/include/base/UpdateDisplacedMeshThread.h
@@ -27,6 +27,7 @@ class UpdateDisplacedMeshThread
   UpdateDisplacedMeshThread(DisplacedProblem & problem);
 
   void operator() (const SemiLocalNodeRange & range) const;
+  void operator() (const NodeRange & range) const;
 
 protected:
   DisplacedProblem & _problem;
diff --git a/framework/src/base/Adaptivity.C b/framework/src/base/Adaptivity.C
index 7cbe164c08b4..e20257c3b815 100644
--- a/framework/src/base/Adaptivity.C
+++ b/framework/src/base/Adaptivity.C
@@ -92,8 +92,14 @@ Adaptivity::init(unsigned int steps, unsigned int initial_steps)
 
     if (!_displaced_mesh_refinement)
       _displaced_mesh_refinement = new MeshRefinement(_displaced_problem->mesh());
+
+    // The periodic boundaries pointer allows the MeshRefinement
+    // object to determine elements which are "topological" neighbors,
+    // i.e. neighbors across periodic boundaries, for the purposes of
+    // refinement.
     _displaced_mesh_refinement->set_periodic_boundaries_ptr(_subproblem.getNonlinearSystem().dofMap().get_periodic_boundaries());
 
+    // TODO: This is currently an empty function on the DisplacedProblem... could it be removed?
     _displaced_problem->initAdaptivity();
   }
 }
@@ -154,15 +160,26 @@ Adaptivity::adaptMesh()
         _displaced_mesh_refinement->flag_elements_by_error_fraction (*_error);
     }
 
+    // If the DisplacedProblem is active, undisplace the DisplacedMesh
+    // in preparation for refinement.  We can't safely refine the
+    // DisplacedMesh directly, since the Hilbert keys computed on the
+    // inconsistenly-displaced Mesh are different on different
+    // processors, leading to inconsistent Hilbert keys.  We must do
+    // this before the undisplaced Mesh is refined, so that the
+    // element and node numbering is still consistent.
+    if (_displaced_problem)
+      _displaced_problem->undisplaceMesh();
+
     // Perform refinement and coarsening
     meshChanged = _mesh_refinement->refine_and_coarsen_elements();
 
-    if (_displaced_problem)
+    if (_displaced_problem && meshChanged)
     {
+      // Now do refinement/coarsening
       bool dispMeshChanged = _displaced_mesh_refinement->refine_and_coarsen_elements();
-      if ((meshChanged && !dispMeshChanged) ||
-          (!meshChanged && dispMeshChanged))
-        mooseError("If either undisplaced mesh or displaced mesh changes due to adaptivity, both must change");
+
+      // Since the undisplaced mesh changed, the displaced mesh better have changed!
+      mooseAssert(dispMeshChanged, "Undisplaced mesh changed, but displaced mesh did not!");
     }
 
     if (meshChanged && _print_mesh_changed)
@@ -200,7 +217,12 @@ Adaptivity::uniformRefine(unsigned int level)
   // we have to go step by step so EquationSystems::reinit() won't freak out
   for (unsigned int i = 0; i < level; i++)
   {
+    // See comment above about why refining the displaced mesh is potentially unsafe.
+    if (_displaced_problem)
+      _displaced_problem->undisplaceMesh();
+
     mesh_refinement.uniformly_refine(1);
+
     if (_displaced_problem)
       displaced_mesh_refinement.uniformly_refine(1);
     _subproblem.meshChanged();
diff --git a/framework/src/base/DisplacedProblem.C b/framework/src/base/DisplacedProblem.C
index e03bdb0364bd..b32ea600ae34 100644
--- a/framework/src/base/DisplacedProblem.C
+++ b/framework/src/base/DisplacedProblem.C
@@ -575,3 +575,26 @@ DisplacedProblem::registerRecoverableData(std::string name)
 
   _mproblem.registerRecoverableData(name);
 }
+
+void
+DisplacedProblem::undisplaceMesh()
+{
+  // If undisplaceMesh() is called during initial adaptivity, it is
+  // not valid to call _mesh.getActiveSemiLocalNodeRange() since it is
+  // not set up yet.  So we are creating the Range by hand.
+  //
+  // We must undisplace *all* our nodes to the _ref_mesh
+  // configuration, not just the local ones, since the partitioners
+  // require this.  We are using the GRAIN_SIZE=1 from MooseMesh.C,
+  // not sure how this value was decided upon.
+  //
+  // Note: we don't have to invalidate/update as much stuff as
+  // DisplacedProblem::updateMesh() does, since this will be handled
+  // by a later call to updateMesh().
+  NodeRange node_range(_mesh.getMesh().nodes_begin(),
+                       _mesh.getMesh().nodes_end(),
+                       /*grainsize=*/1);
+
+  // Undisplace the mesh using threads.
+  Threads::parallel_for (node_range, UpdateDisplacedMeshThread(*this));
+}
diff --git a/framework/src/base/UpdateDisplacedMeshThread.C b/framework/src/base/UpdateDisplacedMeshThread.C
index 1340e234fd91..89779c7d0677 100644
--- a/framework/src/base/UpdateDisplacedMeshThread.C
+++ b/framework/src/base/UpdateDisplacedMeshThread.C
@@ -87,3 +87,21 @@ UpdateDisplacedMeshThread::operator() (const SemiLocalNodeRange & range) const
     }
   }
 }
+
+void
+UpdateDisplacedMeshThread::operator() (const NodeRange & range) const
+{
+  NodeRange::const_iterator nd = range.begin();
+
+  for (; nd != range.end(); ++nd)
+  {
+    Node & displaced_node = **nd;
+
+    // Get the same node from the reference mesh.
+    Node & reference_node = _ref_mesh.node(displaced_node.id());
+
+    // Undisplace the node
+    for (unsigned int i=0; i<LIBMESH_DIM; ++i)
+      displaced_node(i) = reference_node(i);
+  }
+}