diff --git a/src/reader/spirv/function.cc b/src/reader/spirv/function.cc
index d91c7e5..d326ead 100644
--- a/src/reader/spirv/function.cc
+++ b/src/reader/spirv/function.cc
@@ -1072,8 +1072,9 @@
     // There should only be one backedge per backedge block.
     uint32_t num_backedges = 0;
 
-    // Track destinations for normal forward edges, either kForward
-    // or kCaseFallThrough
+    // Track destinations for normal forward edges, either kForward,
+    // kCaseFallThrough, or kIfBreak. These count toward the need
+    // to have a merge instruction.
     std::vector<uint32_t> normal_forward_edges;
 
     if (successors.empty() && src_construct.enclosing_continue) {
@@ -1190,6 +1191,14 @@
           }
         }
 
+        // The edge-kind has been finalized.
+
+        if ((edge_kind == EdgeKind::kForward) ||
+            (edge_kind == EdgeKind::kCaseFallThrough) ||
+            (edge_kind == EdgeKind::kIfBreak)) {
+          normal_forward_edges.push_back(dest);
+        }
+
         if ((edge_kind == EdgeKind::kForward) ||
             (edge_kind == EdgeKind::kCaseFallThrough)) {
           // Check for an invalid forward exit out of this construct.
@@ -1220,8 +1229,6 @@
                    << end_block_desc << " " << end_block;
           }
 
-          normal_forward_edges.push_back(dest);
-
           // Check dominance.
 
           //      Look for edges that violate the dominance condition: a branch
diff --git a/src/reader/spirv/function.h b/src/reader/spirv/function.h
index f37f23f..b98eedf 100644
--- a/src/reader/spirv/function.h
+++ b/src/reader/spirv/function.h
@@ -42,6 +42,19 @@
 namespace spirv {
 
 /// Kinds of CFG edges.
+//
+// The edge kinds are used in many ways.
+//
+// For example, consider the edges leaving a basic block and going to distinct
+// targets. If the total number of kForward + kIfBreak + kCaseFallThrough edges
+// is more than 1, then the block must be a structured header, i.e. it needs
+// a merge instruction to declare the control flow divergence and associated
+// reconvergence point.  Those those edge kinds count toward divergence
+// because SPIR-v is designed to easily map back to structured control flow
+// in GLSL (and C).  In GLSL and C, those forward-flow edges don't have a
+// special statement to express them.  The other forward edges: kSwitchBreak,
+// kLoopBreak, and kLoopContinue directly map to 'break', 'break', and
+// 'continue', respectively.
 enum class EdgeKind {
   // A back-edge: An edge from a node to one of its ancestors in a depth-first
   // search from the entry block.
@@ -64,10 +77,7 @@
   kIfBreak,
   // An edge from one switch case to the next sibling switch case.
   kCaseFallThrough,
-  // None of the above. By structured control flow rules, there can be at most
-  // one forward edge leaving a basic block. Otherwise there must have been a
-  // merge instruction declaring the divergence and associated reconvergence
-  // point.
+  // None of the above.
   kForward
 };
 
diff --git a/src/reader/spirv/function_cfg_test.cc b/src/reader/spirv/function_cfg_test.cc
index 7dfcb60..9cc8304 100644
--- a/src/reader/spirv/function_cfg_test.cc
+++ b/src/reader/spirv/function_cfg_test.cc
@@ -6529,8 +6529,9 @@
                  "a structured header (it has no merge instruction)"));
 }
 
-TEST_F(SpvParserTest,
-       FindIfSelectionInternalHeaders_IfBreak_FromThen_ForwardWithinThen) {
+TEST_F(SpvParserTest, ClassifyCFGEdges_IfBreak_FromThen_ForwardWithinThen) {
+  // Arguably SPIR-V allows this configuration. We're debating whether to ban
+  // it.
   // TODO(dneto): We can make this case work, if we injected
   //    if (!cond2) { rest-of-then-body }
   // at block 30
@@ -6554,33 +6555,24 @@
   auto* p = parser(test::Assemble(assembly));
   ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions()) << p->error();
   FunctionEmitter fe(p, *spirv_function(100));
-  EXPECT_TRUE(FlowFindIfSelectionInternalHeaders(&fe));
+  EXPECT_FALSE(FlowClassifyCFGEdges(&fe));
   EXPECT_THAT(fe.block_order(), ElementsAre(10, 20, 80, 99));
 
   auto* bi20 = fe.GetBlockInfo(20);
   ASSERT_NE(bi20, nullptr);
-  ASSERT_NE(bi20->true_head_for, nullptr);
-  EXPECT_EQ(bi20->true_head_for->begin_id, 10u);
-  EXPECT_EQ(bi20->false_head_for, nullptr);
-  EXPECT_EQ(bi20->premerge_head_for, nullptr);
-  EXPECT_EQ(bi20->exclusive_false_head_for, nullptr);
   EXPECT_EQ(bi20->succ_edge.count(80), 1u);
   EXPECT_EQ(bi20->succ_edge[80], EdgeKind::kForward);
   EXPECT_EQ(bi20->succ_edge.count(99), 1u);
   EXPECT_EQ(bi20->succ_edge[99], EdgeKind::kIfBreak);
 
-  auto* bi80 = fe.GetBlockInfo(80);
-  ASSERT_NE(bi80, nullptr);
-  EXPECT_EQ(bi80->true_head_for, nullptr);
-  EXPECT_EQ(bi80->false_head_for, nullptr);
-  EXPECT_EQ(bi80->premerge_head_for, nullptr);
-  EXPECT_EQ(bi80->exclusive_false_head_for, nullptr);
-  EXPECT_EQ(bi80->succ_edge.count(99), 1u);
-  EXPECT_EQ(bi80->succ_edge[99], EdgeKind::kIfBreak);
+  EXPECT_THAT(p->error(),
+              Eq("Control flow diverges at block 20 (to 99, 80) but it is not "
+                 "a structured header (it has no merge instruction)"));
 }
 
-TEST_F(SpvParserTest,
-       FindIfSelectionInternalHeaders_IfBreak_FromElse_ForwardWithinElse) {
+TEST_F(SpvParserTest, ClassifyCFGEdges_IfBreak_FromElse_ForwardWithinElse) {
+  // Arguably SPIR-V allows this configuration. We're debating whether to ban
+  // it.
   // TODO(dneto): We can make this case work, if we injected
   //    if (!cond2) { rest-of-else-body }
   // at block 30
@@ -6607,33 +6599,22 @@
   auto* p = parser(test::Assemble(assembly));
   ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions()) << p->error();
   FunctionEmitter fe(p, *spirv_function(100));
-  EXPECT_TRUE(FlowFindIfSelectionInternalHeaders(&fe));
+  EXPECT_FALSE(FlowClassifyCFGEdges(&fe));
   EXPECT_THAT(fe.block_order(), ElementsAre(10, 20, 30, 80, 99));
 
   auto* bi30 = fe.GetBlockInfo(30);
   ASSERT_NE(bi30, nullptr);
-  EXPECT_EQ(bi30->true_head_for, nullptr);
-  ASSERT_NE(bi30->false_head_for, nullptr);
-  EXPECT_EQ(bi30->false_head_for->begin_id, 10u);
-  EXPECT_EQ(bi30->premerge_head_for, nullptr);
-  EXPECT_EQ(bi30->exclusive_false_head_for, nullptr);
   EXPECT_EQ(bi30->succ_edge.count(80), 1u);
   EXPECT_EQ(bi30->succ_edge[80], EdgeKind::kForward);
   EXPECT_EQ(bi30->succ_edge.count(99), 1u);
   EXPECT_EQ(bi30->succ_edge[99], EdgeKind::kIfBreak);
 
-  auto* bi80 = fe.GetBlockInfo(80);
-  ASSERT_NE(bi80, nullptr);
-  EXPECT_EQ(bi80->true_head_for, nullptr);
-  EXPECT_EQ(bi80->false_head_for, nullptr);
-  EXPECT_EQ(bi80->premerge_head_for, nullptr);
-  EXPECT_EQ(bi80->exclusive_false_head_for, nullptr);
-  EXPECT_EQ(bi80->succ_edge.count(99), 1u);
-  EXPECT_EQ(bi80->succ_edge[99], EdgeKind::kIfBreak);
+  EXPECT_THAT(p->error(),
+              Eq("Control flow diverges at block 30 (to 99, 80) but it is not "
+                 "a structured header (it has no merge instruction)"));
 }
 
-TEST_F(SpvParserTest,
-       FindIfSelectionInternalHeaders_IfBreak_WithForwardToPremerge_IsError) {
+TEST_F(SpvParserTest, ClassifyCFGEdges_IfBreak_WithForwardToPremerge_IsError) {
   auto assembly = CommonTypes() + R"(
      %100 = OpFunction %void None %voidfn
 
@@ -6657,12 +6638,19 @@
   auto* p = parser(test::Assemble(assembly));
   ASSERT_TRUE(p->BuildAndParseInternalModuleExceptFunctions()) << p->error();
   FunctionEmitter fe(p, *spirv_function(100));
-  EXPECT_FALSE(FlowFindIfSelectionInternalHeaders(&fe));
+  EXPECT_FALSE(FlowClassifyCFGEdges(&fe));
   EXPECT_THAT(fe.block_order(), ElementsAre(10, 20, 30, 80, 99));
-  EXPECT_THAT(
-      p->error(),
-      Eq("Block 20 in if-selection headed at block 10 branches to both the "
-         "merge block 99 and also to block 80 later in the selection"));
+
+  auto* bi20 = fe.GetBlockInfo(20);
+  ASSERT_NE(bi20, nullptr);
+  EXPECT_EQ(bi20->succ_edge.count(80), 1u);
+  EXPECT_EQ(bi20->succ_edge[80], EdgeKind::kForward);
+  EXPECT_EQ(bi20->succ_edge.count(99), 1u);
+  EXPECT_EQ(bi20->succ_edge[99], EdgeKind::kIfBreak);
+
+  EXPECT_THAT(p->error(),
+              Eq("Control flow diverges at block 20 (to 99, 80) but it is not "
+                 "a structured header (it has no merge instruction)"));
 }
 
 TEST_F(SpvParserTest, DISABLED_Codegen_IfBreak_FromThen_ForwardWithinThen) {