Index: clang/lib/StaticAnalyzer/Core/BugReporterVisitors.cpp
===================================================================
--- clang/lib/StaticAnalyzer/Core/BugReporterVisitors.cpp
+++ clang/lib/StaticAnalyzer/Core/BugReporterVisitors.cpp
@@ -306,9 +306,14 @@
     ID.AddPointer(RegionOfInterest);
   }
 
+  void* getTag() const {
+    static int Tag = 0;
+    return static_cast<void *>(&Tag);
+  }
+
   std::shared_ptr<PathDiagnosticPiece> VisitNode(const ExplodedNode *N,
                                                  BugReporterContext &BR,
-                                                 BugReport &) override {
+                                                 BugReport &R) override {
 
     const LocationContext *Ctx = N->getLocationContext();
     const StackFrameContext *SCtx = Ctx->getStackFrame();
@@ -322,9 +327,6 @@
     CallEventRef<> Call =
         BR.getStateManager().getCallEventManager().getCaller(SCtx, State);
 
-    if (Call->isInSystemHeader())
-      return nullptr;
-
     // Region of interest corresponds to an IVar, exiting a method
     // which could have written into that IVar, but did not.
     if (const auto *MC = dyn_cast<ObjCMethodCall>(Call)) {
@@ -333,8 +335,8 @@
         if (RegionOfInterest->isSubRegionOf(SelfRegion) &&
             potentiallyWritesIntoIvar(Call->getRuntimeDefinition().getDecl(),
                                       IvarR->getDecl()))
-          return notModifiedDiagnostics(N, {}, SelfRegion, "self",
-                                        /*FirstIsReferenceType=*/false, 1);
+          return emitNoteOrSuppress(R, *Call, N, {}, SelfRegion, "self",
+                                    /*FirstIsReferenceType=*/false, 1);
       }
     }
 
@@ -342,8 +344,8 @@
       const MemRegion *ThisR = CCall->getCXXThisVal().getAsRegion();
       if (RegionOfInterest->isSubRegionOf(ThisR)
           && !CCall->getDecl()->isImplicit())
-        return notModifiedDiagnostics(N, {}, ThisR, "this",
-                                      /*FirstIsReferenceType=*/false, 1);
+        return emitNoteOrSuppress(R, *Call, N, {}, ThisR, "this",
+                                  /*FirstIsReferenceType=*/false, 1);
 
       // Do not generate diagnostics for not modified parameters in
       // constructors.
@@ -359,21 +361,20 @@
 
       int IndirectionLevel = 1;
       QualType T = PVD->getType();
-      while (const MemRegion *R = S.getAsRegion()) {
-        if (RegionOfInterest->isSubRegionOf(R) && !isPointerToConst(T))
-          return notModifiedDiagnostics(N, {}, R, ParamName,
-                                        ParamIsReferenceType, IndirectionLevel);
+      while (const MemRegion *MR = S.getAsRegion()) {
+        if (RegionOfInterest->isSubRegionOf(MR) && !isPointerToConst(T))
+          return emitNoteOrSuppress(R, *Call, N, {}, MR, ParamName,
+                                    ParamIsReferenceType, IndirectionLevel);
 
         QualType PT = T->getPointeeType();
         if (PT.isNull() || PT->isVoidType()) break;
 
         if (const RecordDecl *RD = PT->getAsRecordDecl())
-          if (auto P = findRegionOfInterestInRecord(RD, State, R))
-            return notModifiedDiagnostics(N, *P, RegionOfInterest, ParamName,
-                                          ParamIsReferenceType,
-                                          IndirectionLevel);
+          if (auto P = findRegionOfInterestInRecord(RD, State, MR))
+            return emitNoteOrSuppress(R, *Call, N, *P, RegionOfInterest, ParamName,
+                                      ParamIsReferenceType, IndirectionLevel);
 
-        S = State->getSVal(R, PT);
+        S = State->getSVal(MR, PT);
         T = PT;
         IndirectionLevel++;
       }
@@ -545,9 +546,29 @@
 
   /// \return Diagnostics piece for region not modified in the current function.
   std::shared_ptr<PathDiagnosticPiece>
-  notModifiedDiagnostics(const ExplodedNode *N, const RegionVector &FieldChain,
-                         const MemRegion *MatchedRegion, StringRef FirstElement,
-                         bool FirstIsReferenceType, unsigned IndirectionLevel) {
+  emitNoteOrSuppress(BugReport &R, const CallEvent &Call, const ExplodedNode *N,
+                     const RegionVector &FieldChain,
+                     const MemRegion *MatchedRegion, StringRef FirstElement,
+                     bool FirstIsReferenceType, unsigned IndirectionLevel) {
+    // Optimistically suppress uninitialized value bugs that result
+    // from system headers having a chance to initialize the value
+    // but failing to do so. It's too unlikely a system header's fault.
+    // It's much more likely a situation in which the function has a failure
+    // mode that the user decided not to check. If we want to hunt such
+    // omitted checks, we should provide an explicit function-specific note
+    // describing the precondition under which the function isn't supposed to
+    // initialize its out-parameter, and additionally check that such
+    // precondition can actually be fulfilled on the current path.
+    if (Call.isInSystemHeader()) {
+      // We make an exception for system header functions that have no branches,
+      // i.e. have exactly 3 CFG blocks: begin, all its code, end. Such
+      // functions unconditionally fail to initialize the variable. If they call
+      // other functions that have more paths within them, this suppression
+      // would still apply when we visit these inner functions.
+      if (N->getStackFrame()->getCFG()->size() > 3)
+        R.markInvalid(getTag(), nullptr);
+      return nullptr;
+    }
 
     PathDiagnosticLocation L =
         PathDiagnosticLocation::create(N->getLocation(), SM);
Index: clang/test/Analysis/Inputs/no-store-suppression.h
===================================================================
--- /dev/null
+++ clang/test/Analysis/Inputs/no-store-suppression.h
@@ -0,0 +1,17 @@
+#pragma clang system_header
+
+namespace std {
+class istream {
+public:
+  bool is_eof();
+  char get_char();
+};
+
+istream &operator>>(istream &is, char &c) {
+  if (is.is_eof())
+    return;
+  c = is.get_char();
+}
+
+extern istream cin;
+};
Index: clang/test/Analysis/no-store-suppression.cpp
===================================================================
--- /dev/null
+++ clang/test/Analysis/no-store-suppression.cpp
@@ -0,0 +1,17 @@
+// RUN: %clang_analyze_cc1 -analyzer-checker=core -verify %s
+
+// expected-no-diagnostics
+
+#include "Inputs/no-store-suppression.h"
+
+using namespace std;
+
+namespace value_uninitialized_after_stream_shift {
+void use(char c);
+
+void foo() {
+  char c;
+  std::cin >> c;
+  use(c); // no-warning
+}
+} // namespace value_uninitialized_after_stream_shift