diff --git a/dynare++/integ/cc/smolyak.cc b/dynare++/integ/cc/smolyak.cc
index 6fec35e9c..36e1c267c 100644
--- a/dynare++/integ/cc/smolyak.cc
+++ b/dynare++/integ/cc/smolyak.cc
@@ -112,12 +112,11 @@ SmolyakQuadrature::SmolyakQuadrature(int d, int l, const OneDQuadrature &uq)
   // todo: check |l>1|, |l>=d|
   // todo: check |l>=uquad.miLevel()|, |l<=uquad.maxLevel()|
   int cum = 0;
-  SymmetrySet ss(l-1, d+1);
-  for (symiterator si(ss); !si.isEnd(); ++si)
+  for (auto &si : SymmetrySet(l-1, d+1))
     {
-      if ((*si)[d] <= d-1)
+      if (si[d] <= d-1)
         {
-          IntSequence lev((const IntSequence &)*si, 0, d);
+          IntSequence lev((const IntSequence &) si, 0, d);
           lev.add(1);
           levels.push_back(lev);
           IntSequence levpts(d);
@@ -171,12 +170,11 @@ int
 SmolyakQuadrature::calcNumEvaluations(int lev) const
 {
   int cum = 0;
-  SymmetrySet ss(lev-1, dim+1);
-  for (symiterator si(ss); !si.isEnd(); ++si)
+  for (auto &si : SymmetrySet(lev-1, dim+1))
     {
-      if ((*si)[dim] <= dim-1)
+      if (si[dim] <= dim-1)
         {
-          IntSequence lev((const IntSequence &)*si, 0, dim);
+          IntSequence lev((const IntSequence &) si, 0, dim);
           lev.add(1);
           IntSequence levpts(dim);
           for (int i = 0; i < dim; i++)
diff --git a/dynare++/kord/korder.cc b/dynare++/kord/korder.cc
index 7f4be316a..553f1eb69 100644
--- a/dynare++/kord/korder.cc
+++ b/dynare++/kord/korder.cc
@@ -342,30 +342,27 @@ KOrder::switchToFolded()
 
   int maxdim = g<unfold>().getMaxDim();
   for (int dim = 1; dim <= maxdim; dim++)
-    {
-      SymmetrySet ss(dim, 4);
-      for (symiterator si(ss); !si.isEnd(); ++si)
-        {
-          if ((*si)[2] == 0 && g<unfold>().check(*si))
-            {
-              auto *ft = new FGSTensor(*(g<unfold>().get(*si)));
-              insertDerivative<fold>(ft);
-              if (dim > 1)
-                {
-                  gss<unfold>().remove(*si);
-                  gs<unfold>().remove(*si);
-                  g<unfold>().remove(*si);
-                }
-            }
-          if (G<unfold>().check(*si))
-            {
-              auto *ft = new FGSTensor(*(G<unfold>().get(*si)));
-              G<fold>().insert(ft);
-              if (dim > 1)
-                {
-                  G<fold>().remove(*si);
-                }
-            }
-        }
-    }
+    for (auto &si : SymmetrySet(dim, 4))
+      {
+        if (si[2] == 0 && g<unfold>().check(si))
+          {
+            auto *ft = new FGSTensor(*(g<unfold>().get(si)));
+            insertDerivative<fold>(ft);
+            if (dim > 1)
+              {
+                gss<unfold>().remove(si);
+                gs<unfold>().remove(si);
+                g<unfold>().remove(si);
+              }
+          }
+        if (G<unfold>().check(si))
+          {
+            auto *ft = new FGSTensor(*(G<unfold>().get(si)));
+            G<fold>().insert(ft);
+            if (dim > 1)
+              {
+                G<fold>().remove(si);
+              }
+          }
+      }
 }
diff --git a/dynare++/kord/korder.hh b/dynare++/kord/korder.hh
index 7c504c00d..784e0c8df 100644
--- a/dynare++/kord/korder.hh
+++ b/dynare++/kord/korder.hh
@@ -871,12 +871,11 @@ KOrder::check(int dim) const
     }
 
   // check for $F_{y^iu^ju'^k}+D_{ijk}+E_{ijk}=0$
-  SymmetrySet ss(dim, 3);
-  for (symiterator si(ss); !si.isEnd(); ++si)
+  for (auto &si : SymmetrySet(dim, 3))
     {
-      int i = (*si)[0];
-      int j = (*si)[1];
-      int k = (*si)[2];
+      int i = si[0];
+      int j = si[1];
+      int k = si[2];
       if (i+j > 0 && k > 0)
         {
           Symmetry sym{i, j, 0, k};
diff --git a/dynare++/kord/korder_stoch.hh b/dynare++/kord/korder_stoch.hh
index 65705afe3..109b1752f 100644
--- a/dynare++/kord/korder_stoch.hh
+++ b/dynare++/kord/korder_stoch.hh
@@ -516,18 +516,17 @@ KOrderStoch::performStep(int order)
   int maxd = g<t>().getMaxDim();
   KORD_RAISE_IF(order-1 != maxd && (order != 1 || maxd != -1),
                 "Wrong order for KOrderStoch::performStep");
-  SymmetrySet ss(order, 4);
-  for (symiterator si(ss); !si.isEnd(); ++si)
+  for (auto &si : SymmetrySet(order, 4))
     {
-      if ((*si)[2] == 0)
+      if (si[2] == 0)
         {
           JournalRecordPair pa(journal);
-          pa << "Recovering symmetry " << *si << endrec;
+          pa << "Recovering symmetry " << si << endrec;
 
-          _Ttensor *G_sym = faaDiBrunoG<t>(*si);
+          _Ttensor *G_sym = faaDiBrunoG<t>(si);
           G<t>().insert(G_sym);
 
-          _Ttensor *g_sym = faaDiBrunoZ<t>(*si);
+          _Ttensor *g_sym = faaDiBrunoZ<t>(si);
           g_sym->mult(-1.0);
           matA.multInv(*g_sym);
           g<t>().insert(g_sym);
diff --git a/dynare++/tl/cc/stack_container.cc b/dynare++/tl/cc/stack_container.cc
index 311f94b05..3bd2ef64f 100644
--- a/dynare++/tl/cc/stack_container.cc
+++ b/dynare++/tl/cc/stack_container.cc
@@ -42,10 +42,10 @@ FoldedStackContainer::multAndAdd(int dim, const FGSContainer &c, FGSTensor &out)
               "Wrong symmetry length of container for FoldedStackContainer::multAndAdd");
 
   sthread::detach_thread_group gr;
-  SymmetrySet ss(dim, c.num());
-  for (symiterator si(ss); !si.isEnd(); ++si)
-    if (c.check(*si))
-      gr.insert(std::make_unique<WorkerFoldMAADense>(*this, *si, c, out));
+
+  for (auto &si : SymmetrySet(dim, c.num()))
+    if (c.check(si))
+      gr.insert(std::make_unique<WorkerFoldMAADense>(*this, si, c, out));
 
   gr.run();
 }
@@ -395,10 +395,9 @@ UnfoldedStackContainer::multAndAdd(int dim, const UGSContainer &c,
               "Wrong symmetry length of container for UnfoldedStackContainer::multAndAdd");
 
   sthread::detach_thread_group gr;
-  SymmetrySet ss(dim, c.num());
-  for (symiterator si(ss); !si.isEnd(); ++si)
-    if (c.check(*si))
-      gr.insert(std::make_unique<WorkerUnfoldMAADense>(*this, *si, c, out));
+  for (auto &si : SymmetrySet(dim, c.num()))
+    if (c.check(si))
+      gr.insert(std::make_unique<WorkerUnfoldMAADense>(*this, si, c, out));
 
   gr.run();
 }
diff --git a/dynare++/tl/cc/symmetry.cc b/dynare++/tl/cc/symmetry.cc
index 9b94df492..23a7e878c 100644
--- a/dynare++/tl/cc/symmetry.cc
+++ b/dynare++/tl/cc/symmetry.cc
@@ -51,53 +51,42 @@ Symmetry::isFull() const
   return count <= 1;
 }
 
-/* Here we construct the beginning of the |symiterator|. The first
-   symmetry index is 0. If length is 2, the second index is the
-   dimension, otherwise we create the subordinal symmetry set and its
-   beginning as subordinal |symiterator|. */
+/* Construct a symiterator of given dimension, starting from the given
+   symmetry. */
 
-symiterator::symiterator(SymmetrySet &ss)
-  : s(ss), end_flag(false)
+symiterator::symiterator(int dim_arg, Symmetry run_arg)
+  : dim{dim_arg}, run(std::move(run_arg))
 {
-  s.sym()[0] = 0;
-  if (s.size() == 2)
-    s.sym()[1] = s.dimen();
-  else
-    {
-      subs = std::make_unique<SymmetrySet>(s, s.dimen());
-      subit = std::make_unique<symiterator>(*subs);
-    }
 }
 
 /* Here we move to the next symmetry. We do so only, if we are not at
    the end. If length is 2, we increase lower index and decrease upper
    index, otherwise we increase the subordinal symmetry. If we got to the
    end, we recreate the subordinal symmetry set and set the subordinal
-   iterator to the beginning. At the end we test, if we are not at the
-   end. This is recognized if the lowest index exceeded the dimension. */
+   iterator to the beginning. */
 
 symiterator &
 symiterator::operator++()
 {
-  if (!end_flag)
+  if (run[0] == dim)
+    run[0]++; // Jump to the past-the-end iterator
+  else if (run.size() == 2)
     {
-      if (s.size() == 2)
+      run[0]++;
+      run[1]--;
+    }
+  else
+    {
+      symiterator subit{dim-run[0], Symmetry(run, run.size()-1)};
+      ++subit;
+      if (run[1] == dim-run[0]+1)
         {
-          s.sym()[0]++;
-          s.sym()[1]--;
+          run[0]++;
+          run[1] = 0;
+          /* subit is equal to the past-the-end iterator, so the range
+             2..(size()-1) is already set to 0 */
+          run[run.size()-1] = dim-run[0];
         }
-      else
-        {
-          ++(*subit);
-          if (subit->isEnd())
-            {
-              s.sym()[0]++;
-              subs = std::make_unique<SymmetrySet>(s, s.dimen()-s.sym()[0]);
-              subit = std::make_unique<symiterator>(*subs);
-            }
-        }
-      if (s.sym()[0] == s.dimen()+1)
-        end_flag = true;
     }
   return *this;
 }
diff --git a/dynare++/tl/cc/symmetry.hh b/dynare++/tl/cc/symmetry.hh
index 2a4976ce7..e5e97bc13 100644
--- a/dynare++/tl/cc/symmetry.hh
+++ b/dynare++/tl/cc/symmetry.hh
@@ -105,95 +105,77 @@ public:
   bool isFull() const;
 };
 
-/* The class |SymmetrySet| defines a set of symmetries of the given
-   length having given dimension. It does not store all the symmetries,
-   rather it provides a storage for one symmetry, which is changed as an
-   adjoint iterator moves.
+/* This is an iterator that iterates over all symmetries of given length and
+   dimension (see the SymmetrySet class for details).
 
-   The iterator class is |symiterator|. It is implemented
-   recursively. The iterator object, when created, creates subordinal
-   iterator, which iterates over a symmetry set whose length is one less,
-   and dimension is the former dimension. When the subordinal iterator
-   goes to its end, the superordinal iterator increases left most index in
-   the symmetry, resets the subordinal symmetry set with different
-   dimension, and iterates through the subordinal symmetry set until its
-   end, and so on. That's why we provide also |SymmetrySet| constructor
-   for construction of a subordinal symmetry set.
+   The beginning iterator is (0, …, 0, dim).
+   Increasing it gives (0, … , 1, dim-1)
+   The just-before-end iterator is (dim, 0, …, 0)
+   The past-the-end iterator is (dim+1, 0, …, 0)
 
-   The typical usage of the abstractions for |SymmetrySet| and
-   |symiterator| is as follows:
-
-   \kern0.3cm
-   \centerline{|for (symiterator si(SymmetrySet(6, 4)); !si.isEnd(); ++si) {body}|}
-   \kern0.3cm
-
-   \noindent It goes through all symmetries of size 4 having dimension
-   6. One can use |*si| as the symmetry in the body. */
-
-class SymmetrySet
-{
-  Symmetry run;
-  int dim;
-public:
-  SymmetrySet(int d, int length)
-    : run(length), dim(d)
-  {
-  }
-  SymmetrySet(SymmetrySet &s, int d)
-    : run(s.run, s.size()-1), dim(d)
-  {
-  }
-  int
-  dimen() const
-  {
-    return dim;
-  }
-  const Symmetry &
-  sym() const
-  {
-    return run;
-  }
-  Symmetry &
-  sym()
-  {
-    return run;
-  }
-  int
-  size() const
-  {
-    return run.size();
-  }
-};
-
-/* The logic of |symiterator| was described in |@<|SymmetrySet| class
-   declaration@>|. Here we only comment that: the class has a reference
-   to the |SymmetrySet| only to know dimension and for access of its
-   symmetry storage. Further we have pointers to subordinal |symiterator|
-   and its |SymmetrySet|. These are pointers, since the recursion ends at
-   length equal to 2, in which case these pointers are uninitialized.
-
-   The constructor creates the iterator which initializes to the first
+   The constructor creates the iterator which starts from the given symmetry
    symmetry (beginning). */
 
 class symiterator
 {
-  SymmetrySet &s;
-  std::unique_ptr<symiterator> subit;
-  std::unique_ptr<SymmetrySet> subs;
-  bool end_flag;
+  const int dim;
+  Symmetry run;
 public:
-  symiterator(SymmetrySet &ss);
+  symiterator(int dim_arg, Symmetry run_arg);
   ~symiterator() = default;
   symiterator &operator++();
-  bool
-  isEnd() const
-  {
-    return end_flag;
-  }
   const Symmetry &
   operator*() const
   {
-    return s.sym();
+    return run;
+  }
+  bool
+  operator=(const symiterator &it)
+  {
+    return dim == it.dim && run == it.run;
+  }
+  bool
+  operator!=(const symiterator &it)
+  {
+    return !operator=(it);
+  }
+};
+
+/* The class |SymmetrySet| defines a set of symmetries of the given length
+   having given dimension (i.e. it represents all the lists of integers of
+   length "len" and of sum equal to "dim"). It does not store all the
+   symmetries, it is just a convenience class for iteration.
+
+   The typical usage of the abstractions for |SymmetrySet| and
+   |symiterator| is as follows:
+
+     for (auto &si : SymmetrySet(6, 4))
+
+   It goes through all symmetries of lenght 4 having dimension 6. One can use
+   "si" as the symmetry in the body. */
+
+class SymmetrySet
+{
+public:
+  const int len;
+  const int dim;
+  SymmetrySet(int dim_arg, int len_arg)
+    : len(len_arg), dim(dim_arg)
+  {
+  }
+  symiterator
+  begin() const
+  {
+    Symmetry run(len);
+    run[len-1] = dim;
+    return { dim, run };
+  }
+  symiterator
+  end() const
+  {
+    Symmetry run(len);
+    run[0] = dim+1;
+    return { dim, run };
   }
 };
 
diff --git a/dynare++/tl/testing/monoms.cc b/dynare++/tl/testing/monoms.cc
index 391f146d0..a8a2c269d 100644
--- a/dynare++/tl/testing/monoms.cc
+++ b/dynare++/tl/testing/monoms.cc
@@ -471,13 +471,12 @@ SparseDerivGenerator::SparseDerivGenerator(
 
   for (int dim = 1; dim <= maxdimen; dim++)
     {
-      SymmetrySet ss(dim, 4);
-      for (symiterator si(ss); !si.isEnd(); ++si)
+      for (auto &si : SymmetrySet(dim, 4))
         {
-          bigg->insert(bigg_m.deriv(*si));
-          rcont->insert(r.deriv(*si));
-          if ((*si)[2] == 0)
-            g->insert(g_m.deriv(*si));
+          bigg->insert(bigg_m.deriv(si));
+          rcont->insert(r.deriv(si));
+          if (si[2] == 0)
+            g->insert(g_m.deriv(si));
         }
 
       ts[dim-1] = f.deriv(dim);
diff --git a/dynare++/tl/testing/tests.cc b/dynare++/tl/testing/tests.cc
index d574fcb01..3bb93092d 100644
--- a/dynare++/tl/testing/tests.cc
+++ b/dynare++/tl/testing/tests.cc
@@ -362,21 +362,19 @@ TestRunnable::fold_zcont(int nf, int ny, int nu, int nup, int nbigg,
 
   for (int d = 2; d <= dim; d++)
     {
-      SymmetrySet ss(d, 4);
-      for (symiterator si(ss); !si.isEnd(); ++si)
+      for (auto &si : SymmetrySet(d, 4))
         {
-          printf("\tSymmetry: "); (*si).print();
-          FGSTensor res(nf, TensorDimens(*si, nvs));
+          printf("\tSymmetry: ");
+          si.print();
+          FGSTensor res(nf, TensorDimens(si, nvs));
           res.getData().zeros();
           clock_t stime = clock();
-          for (int l = 1; l <= (*si).dimen(); l++)
-            {
-              zc.multAndAdd(*(dg.ts[l-1]), res);
-            }
+          for (int l = 1; l <= si.dimen(); l++)
+            zc.multAndAdd(*(dg.ts[l-1]), res);
           stime = clock() - stime;
           printf("\t\ttime for symmetry: %8.4g\n",
                  ((double) stime)/CLOCKS_PER_SEC);
-          const FGSTensor *mres = dg.rcont->get(*si);
+          const FGSTensor *mres = dg.rcont->get(si);
           res.add(-1.0, *mres);
           double normtmp = res.getData().getMax();
           printf("\t\terror normMax:     %10.6g\n", normtmp);
@@ -419,22 +417,20 @@ TestRunnable::unfold_zcont(int nf, int ny, int nu, int nup, int nbigg,
 
   for (int d = 2; d <= dim; d++)
     {
-      SymmetrySet ss(d, 4);
-      for (symiterator si(ss); !si.isEnd(); ++si)
+      for (auto &si : SymmetrySet(d, 4))
         {
-          printf("\tSymmetry: "); (*si).print();
-          UGSTensor res(nf, TensorDimens(*si, nvs));
+          printf("\tSymmetry: ");
+          si.print();
+          UGSTensor res(nf, TensorDimens(si, nvs));
           res.getData().zeros();
           clock_t stime = clock();
-          for (int l = 1; l <= (*si).dimen(); l++)
-            {
-              zc.multAndAdd(*(dg.ts[l-1]), res);
-            }
+          for (int l = 1; l <= si.dimen(); l++)
+            zc.multAndAdd(*(dg.ts[l-1]), res);
           stime = clock() - stime;
           printf("\t\ttime for symmetry: %8.4g\n",
                  ((double) stime)/CLOCKS_PER_SEC);
           FGSTensor fold_res(res);
-          const FGSTensor *mres = dg.rcont->get(*si);
+          const FGSTensor *mres = dg.rcont->get(si);
           fold_res.add(-1.0, *mres);
           double normtmp = fold_res.getData().getMax();
           printf("\t\terror normMax:     %10.6g\n", normtmp);