diff --git a/llvm/test/tools/llvm-objcopy/ELF/segment-test-remove-section.test b/llvm/test/tools/llvm-objcopy/ELF/segment-test-remove-section.test
--- a/llvm/test/tools/llvm-objcopy/ELF/segment-test-remove-section.test
+++ b/llvm/test/tools/llvm-objcopy/ELF/segment-test-remove-section.test
@@ -38,6 +38,8 @@
 ProgramHeaders:
   - Type: PT_LOAD
     Flags: [ PF_X, PF_R ]
+    PAddr: 0x1000
+    VAddr: 0x1000
     Sections:
       - Section: .text
       - Section: .text2
@@ -143,8 +145,8 @@
 #CHECK-NEXT:  ProgramHeader {
 #CHECK-NEXT:    Type: PT_LOAD (0x1)
 #CHECK-NEXT:    Offset: 0x1000
-#CHECK-NEXT:    VirtualAddress: 0x0
-#CHECK-NEXT:    PhysicalAddress: 0x0
+#CHECK-NEXT:    VirtualAddress: 0x1000
+#CHECK-NEXT:    PhysicalAddress: 0x1000
 #CHECK-NEXT:    FileSize: 12288
 #CHECK-NEXT:    MemSize: 12288
 #CHECK-NEXT:    Flags [ (0x5)
diff --git a/llvm/tools/llvm-objcopy/ELF/Object.cpp b/llvm/tools/llvm-objcopy/ELF/Object.cpp
--- a/llvm/tools/llvm-objcopy/ELF/Object.cpp
+++ b/llvm/tools/llvm-objcopy/ELF/Object.cpp
@@ -770,13 +770,21 @@
 // Returns true IFF a section is wholly inside the range of a segment
 static bool sectionWithinSegment(const SectionBase &Section,
                                  const Segment &Segment) {
+  if (!(Section.Flags & SHF_ALLOC))
+    return false;
+
+  bool SectionIsTLS = Section.Flags & SHF_TLS;
+  bool SegmentIsTLS = Segment.Type == PT_TLS;
+  if (SectionIsTLS != SegmentIsTLS)
+    return false;
+
   // If a section is empty it should be treated like it has a size of 1. This is
   // to clarify the case when an empty section lies on a boundary between two
   // segments and ensures that the section "belongs" to the second segment and
   // not the first.
   uint64_t SecSize = Section.Size ? Section.Size : 1;
-  return Segment.Offset <= Section.OriginalOffset &&
-         Segment.Offset + Segment.FileSize >= Section.OriginalOffset + SecSize;
+  return Segment.VAddr <= Section.Addr &&
+         Segment.VAddr + Segment.MemSize >= Section.Addr + SecSize;
 }
 
 // Returns true IFF a segment's original offset is inside of another segment's