diff --git a/llvm/lib/Transforms/IPO/FunctionAttrs.cpp b/llvm/lib/Transforms/IPO/FunctionAttrs.cpp
--- a/llvm/lib/Transforms/IPO/FunctionAttrs.cpp
+++ b/llvm/lib/Transforms/IPO/FunctionAttrs.cpp
@@ -38,6 +38,7 @@
 #include "llvm/IR/BasicBlock.h"
 #include "llvm/IR/Constant.h"
 #include "llvm/IR/Constants.h"
+#include "llvm/IR/Dominators.h"
 #include "llvm/IR/Function.h"
 #include "llvm/IR/InstIterator.h"
 #include "llvm/IR/InstrTypes.h"
@@ -1622,9 +1623,12 @@
         F->doesNotReturn())
       continue;
 
-    // The function can return if any basic blocks can return.
-    // FIXME: this doesn't handle recursion or unreachable blocks.
-    if (none_of(*F, basicBlockCanReturn)) {
+    const DominatorTree DT(*F);
+    if (none_of(*F, [&DT](BasicBlock &BB) {
+          // FIXME: this doesn't handle recursion or infinite loops.
+          return DT.isReachableFromEntry(DT.getNode(&BB)) &&
+                 basicBlockCanReturn(BB);
+        })) {
       F->setDoesNotReturn();
       Changed.insert(F);
     }
diff --git a/llvm/test/Transforms/FunctionAttrs/noreturn.ll b/llvm/test/Transforms/FunctionAttrs/noreturn.ll
--- a/llvm/test/Transforms/FunctionAttrs/noreturn.ll
+++ b/llvm/test/Transforms/FunctionAttrs/noreturn.ll
@@ -40,9 +40,8 @@
   ret i32 %c
 }
 
-; CHECK-NOT: Function Attrs: {{.*}}noreturn
+; CHECK: Function Attrs: {{.*}}noreturn
 ; CHECK: @caller5()
-; We currently don't handle unreachable blocks.
 define i32 @caller5() {
 entry:
   %c = call i32 @noreturn()
@@ -87,4 +86,4 @@
 }
 
 declare token @llvm.coro.id.retcon.once(i32 %size, i32 %align, i8* %buffer, i8* %prototype, i8* %alloc, i8* %free)
-declare i1 @llvm.coro.end(i8*, i1)
\ No newline at end of file
+declare i1 @llvm.coro.end(i8*, i1)