diff --git a/llvm/test/Reduce/remove-bbs-unwinded-to.ll b/llvm/test/Reduce/remove-bbs-unwinded-to.ll
new file mode 100644
index 00000000000000..375678ec99c9db
--- /dev/null
+++ b/llvm/test/Reduce/remove-bbs-unwinded-to.ll
@@ -0,0 +1,39 @@
+; RUN: llvm-reduce --test FileCheck --test-arg --check-prefixes=CHECK-ALL,CHECK-INTERESTINGNESS --test-arg %s --test-arg --input-file %s -o %t
+; RUN: cat %t | FileCheck --check-prefixes=CHECK-ALL,CHECK-FINAL %s
+
+declare i32 @maybe_throwing_callee()
+
+; CHECK-ALL: declare void @did_not_throw(i32)
+declare void @did_not_throw(i32)
+
+declare void @thrown()
+
+; CHECK-ALL: define void @caller()
+define void @caller() personality i8* bitcast (i32 (...)* @__gxx_personality_v0 to i8*) {
+; CHECK-ALL: bb:
+bb:
+; CHECK-INTERESTINGNESS: label %bb3
+; CHECK-FINAL: br label %bb3
+  %i0 = invoke i32 @maybe_throwing_callee()
+          to label %bb3 unwind label %bb1
+
+bb1:
+  landingpad { i8*, i32 } catch i8* null
+  call void @thrown()
+  br label %bb4
+
+; CHECK-ALL: bb3:
+bb3:
+; CHECK-INTERESTINGNESS: call void @did_not_throw(i32
+; CHECK-FINAL: call void @did_not_throw(i32 undef)
+; CHECK-ALL: br label %bb4
+  call void @did_not_throw(i32 %i0)
+  br label %bb4
+
+; CHECK-ALL: bb4:
+; CHECK-ALL: ret void
+bb4:
+  ret void
+}
+
+declare i32 @__gxx_personality_v0(...)
diff --git a/llvm/tools/llvm-reduce/deltas/ReduceBasicBlocks.cpp b/llvm/tools/llvm-reduce/deltas/ReduceBasicBlocks.cpp
index 002d81a6748724..9dee738d4906b0 100644
--- a/llvm/tools/llvm-reduce/deltas/ReduceBasicBlocks.cpp
+++ b/llvm/tools/llvm-reduce/deltas/ReduceBasicBlocks.cpp
@@ -36,11 +36,12 @@ static void replaceBranchTerminator(BasicBlock &BB,
   if (ChunkSucessors.size() == Term->getNumSuccessors())
     return;
 
-  bool IsBranch = isa<BranchInst>(Term);
+  bool IsBranch = isa<BranchInst>(Term) || isa<InvokeInst>(Term);
   Value *Address = nullptr;
   if (auto IndBI = dyn_cast<IndirectBrInst>(Term))
     Address = IndBI->getAddress();
 
+  Term->replaceAllUsesWith(UndefValue::get(Term->getType()));
   Term->eraseFromParent();
 
   if (ChunkSucessors.empty()) {