diff --git a/source/opt/dead_branch_elim_pass.cpp b/source/opt/dead_branch_elim_pass.cpp
index 8425a398cc..16d9fd5636 100644
--- a/source/opt/dead_branch_elim_pass.cpp
+++ b/source/opt/dead_branch_elim_pass.cpp
@@ -167,7 +167,6 @@ bool DeadBranchElimPass::MarkLiveBlocks(
     }
 
     if (simplify) {
-      modified = true;
       conditions_to_simplify.push_back({block, live_lab_id});
       stack.push_back(GetParentBlock(live_lab_id));
     } else {
@@ -179,24 +178,29 @@ bool DeadBranchElimPass::MarkLiveBlocks(
     }
   }
 
-  // Traverse |conditions_to_simplify in reverse order.  This is done so that we
-  // simplify nested constructs before simplifying the constructs that contain
-  // them.
+  // Traverse |conditions_to_simplify| in reverse order.  This is done so that
+  // we simplify nested constructs before simplifying the constructs that
+  // contain them.
   for (auto b = conditions_to_simplify.rbegin();
        b != conditions_to_simplify.rend(); ++b) {
-    SimplifyBranch(b->first, b->second);
+    modified |= SimplifyBranch(b->first, b->second);
   }
 
   return modified;
 }
 
-void DeadBranchElimPass::SimplifyBranch(BasicBlock* block,
+bool DeadBranchElimPass::SimplifyBranch(BasicBlock* block,
                                         uint32_t live_lab_id) {
   Instruction* merge_inst = block->GetMergeInst();
   Instruction* terminator = block->terminator();
   if (merge_inst && merge_inst->opcode() == SpvOpSelectionMerge) {
     if (merge_inst->NextNode()->opcode() == SpvOpSwitch &&
         SwitchHasNestedBreak(block->id())) {
+      if (terminator->NumInOperands() == 2) {
+        // We cannot remove the branch, and it already has a single case, so no
+        // work to do.
+        return false;
+      }
       // We have to keep the switch because it has a nest break, so we
       // remove all cases except for the live one.
       Instruction::OperandList new_operands;
@@ -231,6 +235,7 @@ void DeadBranchElimPass::SimplifyBranch(BasicBlock* block,
     AddBranch(live_lab_id, block);
     context()->KillInst(terminator);
   }
+  return true;
 }
 
 void DeadBranchElimPass::MarkUnreachableStructuredTargets(
@@ -643,7 +648,8 @@ bool DeadBranchElimPass::SwitchHasNestedBreak(uint32_t switch_header_id) {
         if (bb->id() == switch_header_id) {
           return true;
         }
-        return (cfg_analysis->ContainingConstruct(inst) == switch_header_id);
+        return (cfg_analysis->ContainingConstruct(inst) == switch_header_id &&
+                bb->GetMergeInst() == nullptr);
       });
 }
 
diff --git a/source/opt/dead_branch_elim_pass.h b/source/opt/dead_branch_elim_pass.h
index a50933fdb3..7841bc4705 100644
--- a/source/opt/dead_branch_elim_pass.h
+++ b/source/opt/dead_branch_elim_pass.h
@@ -159,14 +159,15 @@ class DeadBranchElimPass : public MemPass {
       std::unordered_set<BasicBlock*>* blocks_with_back_edges);
 
   // Returns true if there is a brach to the merge node of the selection
-  // construct |switch_header_id| that is inside a nested selection construct.
+  // construct |switch_header_id| that is inside a nested selection construct or
+  // in the header of the nested selection construct.
   bool SwitchHasNestedBreak(uint32_t switch_header_id);
 
-  // Replaces the terminator of |block| with a branch to |live_lab_id|.  The
-  // merge instruction is deleted or moved as needed to maintain structured
-  // control flow.  Assumes that the StructuredCFGAnalysis is valid for the
-  // constructs containing |block|.
-  void SimplifyBranch(BasicBlock* block, uint32_t live_lab_id);
+  // Return true of the terminator of |block| is successfully replaced with a
+  // branch to |live_lab_id|.  The merge instruction is deleted or moved as
+  // needed to maintain structured control flow.  Assumes that the
+  // StructuredCFGAnalysis is valid for the constructs containing |block|.
+  bool SimplifyBranch(BasicBlock* block, uint32_t live_lab_id);
 };
 
 }  // namespace opt
diff --git a/test/opt/dead_branch_elim_test.cpp b/test/opt/dead_branch_elim_test.cpp
index e612867620..3dcc0f7701 100644
--- a/test/opt/dead_branch_elim_test.cpp
+++ b/test/opt/dead_branch_elim_test.cpp
@@ -1378,6 +1378,7 @@ OpFunctionEnd
 
   SinglePassRunAndMatch<DeadBranchElimPass>(text, true);
 }
+
 TEST_F(DeadBranchElimTest, LeaveContinueBackedgeExtraBlock) {
   const std::string text = R"(
 ; CHECK: OpBranch [[header:%\w+]]
@@ -3161,6 +3162,73 @@ OpFunctionEnd
   SinglePassRunAndCheck<DeadBranchElimPass>(before, after, true, true);
 }
 
+TEST_F(DeadBranchElimTest, BreakInNestedHeaderWithSingleCase) {
+  const std::string text = R"(OpCapability Shader
+%1 = OpExtInstImport "GLSL.std.450"
+OpMemoryModel Logical GLSL450
+OpEntryPoint Fragment %main "main"
+OpExecutionMode %main OriginUpperLeft
+OpSource GLSL 450
+OpName %main "main"
+%void = OpTypeVoid
+%4 = OpTypeFunction %void
+%bool = OpTypeBool
+%uint = OpTypeInt 32 0
+%uint_0 = OpConstant %uint 0
+%8 = OpUndef %bool
+%main = OpFunction %void None %4
+%9 = OpLabel
+OpSelectionMerge %10 None
+OpSwitch %uint_0 %11
+%11 = OpLabel
+OpSelectionMerge %12 None
+OpBranchConditional %8 %10 %12
+%12 = OpLabel
+OpBranch %10
+%10 = OpLabel
+OpReturn
+OpFunctionEnd
+)";
+
+  SinglePassRunAndCheck<DeadBranchElimPass>(text, text, true, true);
+}
+
+TEST_F(DeadBranchElimTest, BreakInNestedHeaderWithTwoCases) {
+  const std::string text = R"(
+; CHECK: OpSelectionMerge [[merge:%\w+]] None
+; CHECK-NEXT: OpSwitch %uint_0 [[bb:%\w+\n]]
+OpCapability Shader
+%1 = OpExtInstImport "GLSL.std.450"
+OpMemoryModel Logical GLSL450
+OpEntryPoint Fragment %main "main"
+OpExecutionMode %main OriginUpperLeft
+OpSource GLSL 450
+OpName %main "main"
+%void = OpTypeVoid
+%4 = OpTypeFunction %void
+%bool = OpTypeBool
+%uint = OpTypeInt 32 0
+%uint_0 = OpConstant %uint 0
+%8 = OpUndef %bool
+%main = OpFunction %void None %4
+%9 = OpLabel
+OpSelectionMerge %10 None
+OpSwitch %uint_0 %11 1 %12
+%11 = OpLabel
+OpSelectionMerge %13 None
+OpBranchConditional %8 %10 %13
+%13 = OpLabel
+OpBranch %10
+%12 = OpLabel
+OpBranch %10
+%10 = OpLabel
+OpReturn
+OpFunctionEnd
+)";
+
+  SinglePassRunAndMatch<DeadBranchElimPass>(text, true);
+}
+
 // TODO(greg-lunarg): Add tests to verify handling of these cases:
 //
 //    More complex control flow