diff --git a/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/main.c b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/main.c
new file mode 100644
index 00000000000..dbf3eff3989
--- /dev/null
+++ b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/main.c
@@ -0,0 +1,25 @@
+_Bool nondet_bool();
+
+int main()
+{
+  int j = 0;
+  int i;
+L2:
+  ++j;
+  if(j == 2)
+    return 0;
+  int extra_counter = 0;
+  for(int i = nondet_bool() ? -1 : -2; extra_counter < 10; ++i, ++extra_counter)
+  {
+    // The following causes a surprising loop unwinding failure (and an equally
+    // surprising sequence of loop unwinding status output) when using
+    // --unwind 4 --unwinding-assertions
+    // No such failure can be observed when using "goto L2X" instead and
+    // enabling the below label/goto pair.
+    if(i >= 1)
+      goto L2;
+  }
+  //L2X:
+  //   goto L2;
+  return 0;
+}
diff --git a/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/with-transform.desc b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/with-transform.desc
new file mode 100644
index 00000000000..cce4bb55b58
--- /dev/null
+++ b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/with-transform.desc
@@ -0,0 +1,7 @@
+CORE
+main.c
+--ensure-one-backedge-per-target --show-lexical-loops
+^3 is head of \{ 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 \(backedge\) \}$
+^16 is head of \{ 16, 17, 22, 23, 24, 25 \(backedge\) \}$
+^EXIT=0$
+^SIGNAL=0$
diff --git a/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/without-transform.desc b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/without-transform.desc
new file mode 100644
index 00000000000..6a808e9a0e2
--- /dev/null
+++ b/regression/goto-instrument/ensure-one-backedge-per-target-not-lexical/without-transform.desc
@@ -0,0 +1,7 @@
+CORE
+main.c
+--show-lexical-loops
+^16 is head of \{ 16, 17, 22, 23, 24, 25 \(backedge\) \}$
+Note not all loops were in lexical loop form
+^EXIT=0$
+^SIGNAL=0$
diff --git a/src/goto-programs/ensure_one_backedge_per_target.cpp b/src/goto-programs/ensure_one_backedge_per_target.cpp
index b88f43e1075..9ffdd045dc7 100644
--- a/src/goto-programs/ensure_one_backedge_per_target.cpp
+++ b/src/goto-programs/ensure_one_backedge_per_target.cpp
@@ -11,6 +11,8 @@ Author: Diffblue Ltd.
 
 #include "ensure_one_backedge_per_target.h"
 
+#include <analyses/natural_loops.h>
+
 #include "goto_model.h"
 
 #include <algorithm>
@@ -84,9 +86,89 @@ bool ensure_one_backedge_per_target(
   return true;
 }
 
+struct instruction_location_numbert : public goto_programt::targett
+{
+  // Implicit conversion from a goto_programt::targett is permitted.
+  // NOLINTNEXTLINE(runtime/explicit)
+  instruction_location_numbert(goto_programt::targett target)
+    : goto_programt::targett(target)
+  {
+  }
+
+  instruction_location_numbert() = default;
+};
+
+inline bool operator<(
+  const instruction_location_numbert &i1,
+  const instruction_location_numbert &i2)
+{
+  return i1->location_number < i2->location_number;
+}
+
 bool ensure_one_backedge_per_target(goto_programt &goto_program)
 {
-  bool any_change = false;
+  natural_loops_templatet<goto_programt, instruction_location_numbert>
+    natural_loops{goto_program};
+  std::set<instruction_location_numbert> modified_loops;
+
+  for(auto it1 = natural_loops.loop_map.begin();
+      it1 != natural_loops.loop_map.end();
+      ++it1)
+  {
+    DATA_INVARIANT(!it1->second.empty(), "loops cannot have no instructions");
+    // skip over lexical loops
+    if(
+      (*std::prev(it1->second.end()))->is_goto() &&
+      (*std::prev(it1->second.end()))->get_target() == it1->first)
+      continue;
+    if(modified_loops.find(it1->first) != modified_loops.end())
+      continue;
+    // it1 refers to a loop that isn't a lexical loop, now see whether any other
+    // loop is nested within it1
+    for(auto it2 = natural_loops.loop_map.begin();
+        it2 != natural_loops.loop_map.end();
+        ++it2)
+    {
+      if(it1 == it2)
+        continue;
+
+      if(std::includes(
+           it1->second.begin(),
+           it1->second.end(),
+           it2->second.begin(),
+           it2->second.end()))
+      {
+        // make sure that loops with overlapping body are properly nested by a
+        // back edge; this will be a disconnected edge, which
+        // ensure_one_backedge_per_target connects
+        if(
+          modified_loops.find(it2->first) == modified_loops.end() &&
+          (!(*std::prev(it2->second.end()))->is_goto() ||
+           (*std::prev(it2->second.end()))->get_target() != it2->first))
+        {
+          auto new_goto = goto_program.insert_after(
+            *std::prev(it2->second.end()),
+            goto_programt::make_goto(
+              it2->first, (*std::prev(it2->second.end()))->source_location()));
+          it2->second.insert_instruction(new_goto);
+          it1->second.insert_instruction(new_goto);
+          modified_loops.insert(it2->first);
+        }
+
+        goto_program.insert_after(
+          *std::prev(it1->second.end()),
+          goto_programt::make_goto(
+            it1->first, (*std::prev(it1->second.end()))->source_location()));
+        modified_loops.insert(it1->first);
+        break;
+      }
+    }
+  }
+
+  if(!modified_loops.empty())
+    goto_program.update();
+
+  bool any_change = !modified_loops.empty();
 
   for(auto it = goto_program.instructions.begin();
       it != goto_program.instructions.end();