Index: include/llvm/IR/Function.h
===================================================================
--- include/llvm/IR/Function.h
+++ include/llvm/IR/Function.h
@@ -339,6 +339,9 @@
   void setConvergent() {
     addFnAttr(Attribute::Convergent);
   }
+  void setNotConvergent() {
+    removeFnAttr(Attribute::Convergent);
+  }
 
   /// Determine if the function is known not to recurse, directly or
   /// indirectly.
Index: lib/Transforms/IPO/FunctionAttrs.cpp
===================================================================
--- lib/Transforms/IPO/FunctionAttrs.cpp
+++ lib/Transforms/IPO/FunctionAttrs.cpp
@@ -930,6 +930,35 @@
   return MadeChange;
 }
 
+/// Remove convergent attributes where we can prove that none of our callees are
+/// themselves convergent.
+static bool removeConvergentAttrs(const CallGraphSCC &SCC) {
+  const CallGraphNode *CGN = *SCC.begin();
+  Function *F = CGN->getFunction();
+  if (!F || F->isDeclaration() || !F->isConvergent()) return false;
+
+  // We can't mark F as not-convergent if any of its callees are convergent.
+  if (llvm::any_of(*CGN, [](const CallGraphNode::CallRecord &CR) {
+        Function *F = CR.second->getFunction();
+        return !F || F->isConvergent();
+      }))
+    return false;
+
+  // CGN doesn't contain calls to intrinsics, so we have to iterate over F's
+  // body looking for those.
+  for (auto &BB : *F)
+    for (auto &I : BB) {
+      CallSite CS(cast<Value>(&I));
+      if (!CS) continue;
+      Function *Callee = CS.getCalledFunction();
+      if (Callee && Callee->isIntrinsic() && Callee->isConvergent())
+        return false;
+    }
+
+  F->setNotConvergent();
+  return true;
+}
+
 static bool setDoesNotRecurse(Function &F) {
   if (F.doesNotRecurse())
     return false;
@@ -1006,6 +1035,7 @@
   if (!ExternalNode) {
     Changed |= addNoAliasAttrs(SCCNodes);
     Changed |= addNonNullAttrs(SCCNodes, *TLI);
+    Changed |= removeConvergentAttrs(SCC);
   }
 
   Changed |= addNoRecurseAttrs(SCC);
Index: test/Transforms/FunctionAttrs/convergent.ll
===================================================================
--- /dev/null
+++ test/Transforms/FunctionAttrs/convergent.ll
@@ -0,0 +1,43 @@
+; RUN: opt < %s -basicaa -functionattrs -rpo-functionattrs -S | FileCheck %s
+
+; CHECK define i32 @nonleaf() #0
+define i32 @nonleaf() convergent {
+  %a = call i32 @leaf()
+  ret i32 %a
+}
+
+; CHECK: define i32 @leaf() #0
+define i32 @leaf() convergent {
+  ret i32 0
+}
+
+declare i32 @k() convergent
+; CHECK: define i32 @extern() #1
+define i32 @extern() convergent {
+  %a = call i32 @k()
+  ret i32 %a
+}
+
+define i32 @call_extern() convergent {
+  %a = call i32 @extern()
+  ret i32 %a
+}
+
+declare void @llvm.cuda.syncthreads() convergent
+; CHECK: define i32 @intrinsic() #3
+define i32 @intrinsic() convergent {
+  call void @llvm.cuda.syncthreads()
+  ret i32 0
+}
+
+@xyz = global i32 ()* null
+; CHECK: define i32 @functionptr() #1 {
+define i32 @functionptr() convergent {
+  %1 = load i32 ()*, i32 ()** @xyz
+  %2 = call i32 %1()
+  ret i32 %2
+}
+
+; CHECK: attributes #0 = { norecurse readnone }
+; CHECK: attributes #1 = { convergent }
+; CHECK: attributes #3 = { convergent norecurse }