diff --git a/test/tools/llvm-objcopy/COFF/Inputs/discard-locals.yaml b/test/tools/llvm-objcopy/COFF/Inputs/discard-locals.yaml
new file mode 100644
index 0000000..6a80935
--- /dev/null
+++ b/test/tools/llvm-objcopy/COFF/Inputs/discard-locals.yaml
@@ -0,0 +1,45 @@
+--- !COFF
+header:          
+  Machine:         IMAGE_FILE_MACHINE_AMD64
+  Characteristics: [  ]
+sections:        
+  - Name:            .text
+    Characteristics: [  ]
+    Alignment:       4
+    SectionData:     E800000000C3C3C3
+    Relocations:     
+      - VirtualAddress:  1
+        SymbolName:      local_referenced
+        Type:            IMAGE_REL_AMD64_REL32
+symbols:         
+  - Name:            external
+    Value:           0
+    SectionNumber:   1
+    SimpleType:      IMAGE_SYM_TYPE_NULL
+    ComplexType:     IMAGE_SYM_DTYPE_NULL
+    StorageClass:    IMAGE_SYM_CLASS_EXTERNAL
+  - Name:            external_undefined
+    Value:           0
+    SectionNumber:   0
+    SimpleType:      IMAGE_SYM_TYPE_NULL
+    ComplexType:     IMAGE_SYM_DTYPE_NULL
+    StorageClass:    IMAGE_SYM_CLASS_EXTERNAL
+  - Name:            local_unreferenced
+    Value:           6
+    SectionNumber:   1
+    SimpleType:      IMAGE_SYM_TYPE_NULL
+    ComplexType:     IMAGE_SYM_DTYPE_NULL
+    StorageClass:    IMAGE_SYM_CLASS_STATIC
+  - Name:            local_referenced
+    Value:           7
+    SectionNumber:   1
+    SimpleType:      IMAGE_SYM_TYPE_NULL
+    ComplexType:     IMAGE_SYM_DTYPE_NULL
+    StorageClass:    IMAGE_SYM_CLASS_STATIC
+  - Name:            local_undefined_unreferenced
+    Value:           0
+    SectionNumber:   0
+    SimpleType:      IMAGE_SYM_TYPE_NULL
+    ComplexType:     IMAGE_SYM_DTYPE_NULL
+    StorageClass:    IMAGE_SYM_CLASS_STATIC
+...
diff --git a/test/tools/llvm-objcopy/COFF/discard-all.test b/test/tools/llvm-objcopy/COFF/discard-all.test
new file mode 100644
index 0000000..b375c52
--- /dev/null
+++ b/test/tools/llvm-objcopy/COFF/discard-all.test
@@ -0,0 +1,25 @@
+RUN: yaml2obj %p/Inputs/discard-locals.yaml > %t.in.o
+
+RUN: llvm-objdump -t %t.in.o | FileCheck %s --check-prefixes=SYMBOLS,SYMBOLS-PRE
+
+RUN: llvm-objcopy --discard-all %t.in.o %t.out.o
+RUN: llvm-objdump -t %t.out.o | FileCheck %s --check-prefixes=SYMBOLS
+
+RUN: llvm-objcopy -x %t.in.o %t.out-x.o
+RUN: cmp %t.out.o %t.out-x.o
+
+RUN: cp %t.in.o %t.strip-x.o
+RUN: llvm-strip -x %t.strip-x.o
+RUN: cmp %t.out.o %t.strip-x.o
+
+RUN: cp %t.in.o %t.strip-discard-all.o
+RUN: llvm-strip --discard-all %t.strip-discard-all.o
+RUN: cmp %t.out.o %t.strip-discard-all.o
+
+SYMBOLS: SYMBOL TABLE:
+SYMBOLS-NEXT: external
+SYMBOLS-NEXT: external_undefined
+SYMBOLS-PRE-NEXT: local_unreferenced
+SYMBOLS-NEXT: local_referenced
+SYMBOLS-NEXT: local_undefined_unreferenced
+SYMBOLS-EMPTY:
diff --git a/test/tools/llvm-objcopy/COFF/strip-unneeded.test b/test/tools/llvm-objcopy/COFF/strip-unneeded.test
new file mode 100644
index 0000000..7700449
--- /dev/null
+++ b/test/tools/llvm-objcopy/COFF/strip-unneeded.test
@@ -0,0 +1,14 @@
+RUN: yaml2obj %p/Inputs/discard-locals.yaml > %t.in.o
+
+RUN: llvm-objdump -t %t.in.o | FileCheck %s --check-prefixes=SYMBOLS,SYMBOLS-PRE
+
+RUN: llvm-objcopy --strip-unneeded %t.in.o %t.out.o
+RUN: llvm-objdump -t %t.out.o | FileCheck %s --check-prefix=SYMBOLS
+
+SYMBOLS: SYMBOL TABLE:
+SYMBOLS-NEXT: external
+SYMBOLS-NEXT: external_undefined
+SYMBOLS-PRE-NEXT: local_unreferenced
+SYMBOLS-NEXT: local_referenced
+SYMBOLS-PRE-NEXT: local_undefined_unreferenced
+SYMBOLS-EMPTY:
diff --git a/tools/llvm-objcopy/COFF/COFFObjcopy.cpp b/tools/llvm-objcopy/COFF/COFFObjcopy.cpp
index 9087cf6..d48bd02 100644
--- a/tools/llvm-objcopy/COFF/COFFObjcopy.cpp
+++ b/tools/llvm-objcopy/COFF/COFFObjcopy.cpp
@@ -29,7 +29,8 @@
 
 static Error handleArgs(const CopyConfig &Config, Object &Obj) {
   // If we need to do per-symbol removals, initialize the Referenced field.
-  if (!Config.SymbolsToRemove.empty())
+  if (Config.StripUnneeded || Config.DiscardAll ||
+      !Config.SymbolsToRemove.empty())
     if (Error E = Obj.markSymbols())
       return E;
 
@@ -46,6 +47,16 @@
       return true;
     }
 
+    if (!Sym.Referenced && Sym.Sym.StorageClass == IMAGE_SYM_CLASS_STATIC) {
+      if (Config.StripUnneeded)
+        return true;
+      // GNU objcopy keeps referenced local symbols and external symbols
+      // if --discard-all is set, similar to what --strip-unneeded does,
+      // but undefined local symbols are kept when --discard-all is set.
+      if (Config.DiscardAll && Sym.Sym.SectionNumber != 0)
+        return true;
+    }
+
     return false;
   });
   return Error::success();