Index: test/tools/llvm-objcopy/ELF/compress-debug-sections-zlib-header.test
===================================================================
--- /dev/null
+++ test/tools/llvm-objcopy/ELF/compress-debug-sections-zlib-header.test
@@ -0,0 +1,44 @@
+# REQUIRES: zlib
+
+# RUN: yaml2obj %s -o %t1.o
+# RUN: llvm-objcopy --compress-debug-sections %t1.o %t2.o
+# RUN: llvm-readobj -s %t2.o | FileCheck %s
+
+# We had a bug when llvm-objdump did not compress normally named sections
+# that had data which started from "ZLIB". Such header is used in zlib-gnu
+# compression format, but the sign of using is not the header, but section name,
+# first of all. The name of the compressed section should start from .z* (e.g .zdebug_info).
+# If it does not start from that bytes, it is not a zlib-gnu format.
+
+# In this test we have 2 normal sections, one of them starts from "ZLIB",
+# another starts from "ZZZZ". Check we compress both as expected.
+
+# CHECK:        Name: .debug_foo
+# CHECK-NEXT:   Type: SHT_PROGBITS
+# CHECK-NEXT:   Flags [
+# CHECK-NEXT:     SHF_COMPRESSED
+# CHECK-NEXT:   ]
+
+# CHECK:        Name: .debug_bar
+# CHECK-NEXT:   Type: SHT_PROGBITS
+# CHECK-NEXT:   Flags [
+# CHECK-NEXT:     SHF_COMPRESSED
+# CHECK-NEXT:   ]
+
+--- !ELF
+FileHeader:      
+  Class:           ELFCLASS64
+  Data:            ELFDATA2LSB
+  Type:            ET_REL
+  Machine:         EM_X86_64
+Sections:        
+  - Name:            .debug_foo
+    Type:            SHT_PROGBITS
+    AddressAlign:    0x0000000000000001
+    # "ZLIB"
+    Content:         5A4C49420000000000000000
+  - Name:            .debug_bar
+    Type:            SHT_PROGBITS
+    AddressAlign:    0x0000000000000001
+    # "ZZZZ"
+    Content:         5A5A5A5A0000000000000000
Index: tools/llvm-objcopy/ELF/ELFObjcopy.cpp
===================================================================
--- tools/llvm-objcopy/ELF/ELFObjcopy.cpp
+++ tools/llvm-objcopy/ELF/ELFObjcopy.cpp
@@ -223,18 +223,11 @@
   return createStringError(object_error::parse_failed, "Section not found");
 }
 
-static bool isCompressed(const SectionBase &Section) {
-  const char *Magic = "ZLIB";
-  return StringRef(Section.Name).startswith(".zdebug") ||
-         (Section.OriginalData.size() > strlen(Magic) &&
-          !strncmp(reinterpret_cast<const char *>(Section.OriginalData.data()),
-                   Magic, strlen(Magic))) ||
-         (Section.Flags & ELF::SHF_COMPRESSED);
-}
-
 static bool isCompressable(const SectionBase &Section) {
-  return !isCompressed(Section) && isDebugSection(Section) &&
-         Section.Name != ".gdb_index";
+  if ((Section.Flags & ELF::SHF_COMPRESSED) ||
+      StringRef(Section.Name).startswith(".zdebug"))
+    return false;
+  return isDebugSection(Section) && Section.Name != ".gdb_index";
 }
 
 static void replaceDebugSections(