diff --git a/jbmc/src/java_bytecode/java_local_variable_table.cpp b/jbmc/src/java_bytecode/java_local_variable_table.cpp
index d3822c3abed..7e542b52f28 100644
--- a/jbmc/src/java_bytecode/java_local_variable_table.cpp
+++ b/jbmc/src/java_bytecode/java_local_variable_table.cpp
@@ -467,9 +467,13 @@ static java_bytecode_convert_methodt::method_offsett get_common_dominator(
       dominator_analysis.cfg.entry_map.at(v->var.start_pc);
     const auto &this_var_doms=
       dominator_analysis.cfg[dominator_nodeidx].dominators;
-    for(const auto this_var_dom : this_var_doms)
-      if(this_var_dom<=first_pc)
-        candidate_dominators.push_back(this_var_dom);
+    this_var_doms.for_each(
+      [&candidate_dominators, first_pc](
+        const java_bytecode_convert_methodt::method_offsett &this_var_dom)
+      {
+        if(this_var_dom <= first_pc)
+          candidate_dominators.push_back(this_var_dom);
+      });
   }
   std::sort(candidate_dominators.begin(), candidate_dominators.end());
 
diff --git a/src/analyses/cfg_dominators.h b/src/analyses/cfg_dominators.h
index 6114ea90f82..3008fe8fa11 100644
--- a/src/analyses/cfg_dominators.h
+++ b/src/analyses/cfg_dominators.h
@@ -12,14 +12,17 @@ Author: Georg Weissenbacher, georg@weissenbacher.name
 #ifndef CPROVER_ANALYSES_CFG_DOMINATORS_H
 #define CPROVER_ANALYSES_CFG_DOMINATORS_H
 
-#include <set>
-#include <list>
-#include <map>
-#include <iosfwd>
+#include <util/sharing_map.h>
 
+#include <goto-programs/cfg.h>
 #include <goto-programs/goto_functions.h>
 #include <goto-programs/goto_program.h>
-#include <goto-programs/cfg.h>
+
+#include <algorithm>
+#include <iosfwd>
+#include <list>
+#include <map>
+#include <vector>
 
 /// Dominator graph. This computes a control-flow graph (see \ref cfgt) and
 /// decorates it with dominator sets per program point, following
@@ -36,7 +39,97 @@ template <class P, class T, bool post_dom>
 class cfg_dominators_templatet
 {
 public:
-  typedef std::set<T, typename P::target_less_than> target_sett;
+  /// Set of program points, backed by a copy-on-write sharing map so that
+  /// similar sets share most of their representation. Dominator sets of
+  /// adjacent program points typically differ in just a single element, so
+  /// the sharing keeps the total memory linear-ish in the program size, where
+  /// explicit per-node `std::set`s are worst-case quadratic (a straight-line
+  /// program of N instructions has dominator sets of total size N^2/2, which
+  /// for machine-generated functions with ~100k instructions exhausts tens of
+  /// gigabytes of memory).
+  class target_sett
+  {
+  public:
+    bool empty() const
+    {
+      return map.empty();
+    }
+
+    std::size_t size() const
+    {
+      return map.size();
+    }
+
+    std::size_t count(const T &t) const
+    {
+      return map.has_key(t) ? 1 : 0;
+    }
+
+    void insert(const T &t)
+    {
+      if(!map.has_key(t))
+        map.insert(t, unitt{});
+    }
+
+    /// Invoke \p f for each element of the set, in no particular order.
+    void for_each(std::function<void(const T &)> f) const
+    {
+      map.iterate([&f](const T &k, const unitt &) { f(k); });
+    }
+
+    /// Remove all elements that are not also contained in \p other, except
+    /// that \p keep is always retained. Return true if any element was
+    /// removed. The delta view used here only visits elements in subtrees
+    /// that are not shared between the two maps, so intersecting largely
+    /// overlapping sets is much cheaper than element-wise iteration.
+    bool intersect_with(const target_sett &other, const T &keep)
+    {
+      typename mapt::delta_viewt delta_view;
+      map.get_delta_view(other.map, delta_view, false);
+
+      std::vector<T> to_erase;
+      for(const auto &delta_item : delta_view)
+      {
+        if(!delta_item.is_in_both_maps() && !(delta_item.k == keep))
+          to_erase.push_back(delta_item.k);
+      }
+
+      for(const auto &item : to_erase)
+        map.erase(item);
+
+      return !to_erase.empty();
+    }
+
+  protected:
+    struct unitt
+    {
+    };
+
+    struct target_hasht
+    {
+      /// Program-point hash: program points are either integral (e.g. Java
+      /// bytecode offsets) or iterator-like (e.g. goto-program targets), so
+      /// hash the value itself or the address of the object it refers to,
+      /// respectively.
+      template <typename U = T>
+      typename std::enable_if<std::is_integral<U>::value, std::size_t>::type
+      operator()(const U &t) const
+      {
+        return std::hash<U>{}(t);
+      }
+
+      template <typename U = T>
+      typename std::enable_if<!std::is_integral<U>::value, std::size_t>::type
+      operator()(const U &t) const
+      {
+        return std::hash<const void *>{}(&*t);
+      }
+    };
+
+    typedef sharing_mapt<T, unitt, false, target_hasht> mapt;
+
+    mapt map;
+  };
 
   struct nodet
   {
@@ -210,38 +303,7 @@ void cfg_dominators_templatet<P, T, post_dom>::fixedpoint(P &program)
       if(other.empty())
         continue;
 
-      typename target_sett::const_iterator n_it=node.dominators.begin();
-      typename target_sett::const_iterator o_it=other.begin();
-
-      // in-place intersection. not safe to use set_intersect
-      while(n_it!=node.dominators.end() && o_it!=other.end())
-      {
-        if(*n_it==current)
-          ++n_it;
-        else if(typename P::target_less_than()(*n_it, *o_it))
-        {
-          changed=true;
-          node.dominators.erase(n_it++);
-        }
-        else if(typename P::target_less_than()(*o_it, *n_it))
-          ++o_it;
-        else
-        {
-          ++n_it;
-          ++o_it;
-        }
-      }
-
-      while(n_it!=node.dominators.end())
-      {
-        if(*n_it==current)
-          ++n_it;
-        else
-        {
-          changed=true;
-          node.dominators.erase(n_it++);
-        }
-      }
+      changed |= node.dominators.intersect_with(other, current);
     }
 
     if(changed) // fixed point for node reached?
@@ -284,8 +346,17 @@ void cfg_dominators_templatet<P, T, post_dom>::output(std::ostream &out) const
       out << " post-dominated by ";
     else
       out << " dominated by ";
+
+    std::vector<T> sorted_dominators;
+    cfg[node.second].dominators.for_each([&sorted_dominators](const T &d)
+                                         { sorted_dominators.push_back(d); });
+    std::sort(
+      sorted_dominators.begin(),
+      sorted_dominators.end(),
+      typename P::target_less_than{});
+
     bool first=true;
-    for(const auto &d : cfg[node.second].dominators)
+    for(const auto &d : sorted_dominators)
     {
       if(!first)
         out << ", ";
diff --git a/src/analyses/dependence_graph.cpp b/src/analyses/dependence_graph.cpp
index efb7c6ae8fc..dffa26d60bd 100644
--- a/src/analyses/dependence_graph.cpp
+++ b/src/analyses/dependence_graph.cpp
@@ -107,7 +107,7 @@ void dep_graph_domaint::control_dependencies(
       const cfg_post_dominatorst::cfgt::nodet &m_s=
         pd.cfg[edge.first];
 
-      if(m_s.dominators.find(to)!=m_s.dominators.end())
+      if(m_s.dominators.count(to) != 0)
         post_dom_one=true;
       else
         post_dom_all=false;
diff --git a/src/analyses/sese_regions.cpp b/src/analyses/sese_regions.cpp
index 240d5667845..d64a6f07d5a 100644
--- a/src/analyses/sese_regions.cpp
+++ b/src/analyses/sese_regions.cpp
@@ -146,10 +146,21 @@ void sese_region_analysist::compute_sese_regions(
     // but our current dominator analysis doesn't make it easy to determine an
     // immediate dominator.
 
+    // Iterate in a deterministic (location-number) order, since ties on the
+    // dominator-set size below are broken by iteration order.
+    std::vector<goto_programt::const_targett> sorted_postdoms;
+    instruction_postdoms.for_each(
+      [&sorted_postdoms](const goto_programt::const_targett &d)
+      { sorted_postdoms.push_back(d); });
+    std::sort(
+      sorted_postdoms.begin(),
+      sorted_postdoms.end(),
+      goto_programt::target_less_than{});
+
     // Ideally I would use `std::optional<std::size_t>` here, but it triggers a
     // GCC-5 bug.
     std::size_t closest_exit_index = dominators.cfg.size();
-    for(const auto &possible_exit : instruction_postdoms)
+    for(const auto &possible_exit : sorted_postdoms)
     {
       const auto possible_exit_index = dominators.get_node_index(possible_exit);
       const auto &possible_exit_node = dominators.cfg[possible_exit_index];
diff --git a/src/analyses/variable-sensitivity/variable_sensitivity_dependence_graph.cpp b/src/analyses/variable-sensitivity/variable_sensitivity_dependence_graph.cpp
index 80afe243632..8a18ed15ed2 100644
--- a/src/analyses/variable-sensitivity/variable_sensitivity_dependence_graph.cpp
+++ b/src/analyses/variable-sensitivity/variable_sensitivity_dependence_graph.cpp
@@ -272,7 +272,7 @@ void variable_sensitivity_dependence_domaint::control_dependencies(
     {
       const cfg_post_dominatorst::cfgt::nodet &m_s = pd.cfg[edge.first];
 
-      if(m_s.dominators.find(to) != m_s.dominators.end())
+      if(m_s.dominators.count(to) != 0)
         post_dom_one = true;
       else
         post_dom_all = false;
diff --git a/src/goto-instrument/full_slicer.cpp b/src/goto-instrument/full_slicer.cpp
index 736864cdc9d..2e661ec2365 100644
--- a/src/goto-instrument/full_slicer.cpp
+++ b/src/goto-instrument/full_slicer.cpp
@@ -155,23 +155,31 @@ void full_slicert::add_jumps(
       // lex_succ
       goto_programt::const_targett nearest=lex_succ;
       std::size_t post_dom_size=0;
-      for(cfg_dominatorst::target_sett::const_iterator d_it =
-            j_PC_node.dominators.begin();
-          d_it != j_PC_node.dominators.end();
-          ++d_it)
+      // Iterate over the dominators in a deterministic (location-number)
+      // order, since ties on `post_dom_size` below are broken by iteration
+      // order.
+      std::vector<goto_programt::const_targett> sorted_dominators;
+      j_PC_node.dominators.for_each(
+        [&sorted_dominators](const goto_programt::const_targett &dominator)
+        { sorted_dominators.push_back(dominator); });
+      std::sort(
+        sorted_dominators.begin(),
+        sorted_dominators.end(),
+        goto_programt::target_less_than{});
+      for(const auto &dominator : sorted_dominators)
       {
-        const auto &node = cfg.get_node(*d_it);
+        const auto &node = cfg.get_node(dominator);
         if(node.node_required)
         {
           const irep_idt &id2 = node.function_id;
           INVARIANT(id==id2,
                     "goto/jump expected to be within a single function");
 
-          const auto &postdom_node = pd.get_node(*d_it);
+          const auto &postdom_node = pd.get_node(dominator);
 
           if(postdom_node.dominators.size() > post_dom_size)
           {
-            nearest=*d_it;
+            nearest = dominator;
             post_dom_size = postdom_node.dominators.size();
           }
         }