diff --git a/llvm/test/tools/llvm-objcopy/ELF/only-keep-debug.test b/llvm/test/tools/llvm-objcopy/ELF/only-keep-debug.test
--- a/llvm/test/tools/llvm-objcopy/ELF/only-keep-debug.test
+++ b/llvm/test/tools/llvm-objcopy/ELF/only-keep-debug.test
@@ -222,3 +222,73 @@
     Flags: [ SHF_ALLOC ]
 DynamicSymbols: []
 Symbols: []
+
+## PT_TLS and .tdata are empty. Test that we still attribute .tdata to PT_TLS
+## and rewrite p_offset of PT_TLS.
+## If we don't rewrite p_offset of PT_TLS and the deleted bytes are large,
+## p_offset can be larger than the file size, and trigger validation errors.
+# RUN: yaml2obj --docnum=4 %s -o %t4
+# RUN: llvm-objcopy --only-keep-debug %t4 %t4.dbg
+# RUN: llvm-readelf -S -l %t4.dbg | FileCheck --check-prefix=CHECK4 %s
+
+# CHECK4:      [Nr] Name        Type     Address          Off    Size   ES Flg Lk Inf Al
+# CHECK4:      [ 1] .note       NOTE     0000000000000200 000200 000001 00   A  0   0 512
+# CHECK4-NEXT: [ 2] .text       NOBITS   0000000000000201 000201 000001 00  AX  0   0  0
+# CHECK4-NEXT: [ 3] .tdata      NOBITS   0000000000001240 000240 000000 00 WAT  0   0 64
+# CHECK4-NEXT: [ 4] .got        NOBITS   0000000000001240 000240 000008 00  WA  0   0 0
+
+# CHECK4:      Type Offset   VirtAddr           PhysAddr           FileSiz  MemSiz   Flg Align
+# CHECK4-NEXT: LOAD 0x000200 0x0000000000000200 0x0000000000000000 0x000001 0x000002 R E 0x1000
+# CHECK4-NEXT: LOAD 0x000240 0x0000000000001240 0x0000000000000000 0x000000 0x000008 RW  0x1000
+# CHECK4-NEXT: TLS  0x000240 0x0000000000001240 0x0000000000000000 0x000000 0x000000 R   0x40
+
+--- !ELF
+FileHeader:
+  Class:   ELFCLASS64
+  Data:    ELFDATA2LSB
+  Type:    ET_DYN
+  Machine: EM_X86_64
+Sections:
+  - Name:         .note
+    Type:         SHT_NOTE
+    Flags:        [ SHF_ALLOC ]
+    Address:      0x200
+    AddressAlign: 0x200
+    Size:         1
+  - Name:         .text
+    Type:         SHT_PROGBITS
+    Flags:        [ SHF_ALLOC, SHF_EXECINSTR ]
+    Address:      0x201
+    Size:         1
+  - Name:         .tdata
+    Type:         SHT_PROGBITS
+    Flags:        [ SHF_ALLOC, SHF_WRITE, SHF_TLS ]
+    Address:      0x1240   # Ensure Address=0x1000+Offset
+    AddressAlign: 0x40
+  - Name:         .got
+    Type:         SHT_PROGBITS
+    Flags:        [ SHF_ALLOC, SHF_WRITE ]
+    Address:      0x1240
+    Size:         8
+DynamicSymbols: []
+Symbols: []
+ProgramHeaders:
+  - Type:     PT_LOAD
+    Flags:    [ PF_R, PF_X ]
+    VAddr:    0x200
+    Align:    0x1000
+    Sections:
+      - Section: .note
+      - Section: .text
+  - Type:     PT_LOAD
+    Flags:    [ PF_R, PF_W ]
+    VAddr:    0x1240
+    Align:    0x1000
+    Sections:
+      - Section: .tdata
+      - Section: .got
+  - Type:     PT_TLS
+    Flags:    [ PF_R ]
+    VAddr:    0x1240
+    Sections:
+      - Section: .tdata
diff --git a/llvm/test/tools/llvm-objcopy/ELF/strip-all.test b/llvm/test/tools/llvm-objcopy/ELF/strip-all.test
--- a/llvm/test/tools/llvm-objcopy/ELF/strip-all.test
+++ b/llvm/test/tools/llvm-objcopy/ELF/strip-all.test
@@ -74,10 +74,11 @@
     Sections:
       - Section: non_alloc_in_segment
 
-# CHECK: SectionHeaderCount: 6
+# CHECK: SectionHeaderCount: 7
 
 # CHECK: Name: non_alloc_in_segment
 # CHECK: Name: .bss
 # CHECK: Name: .text
+# CHECK: Name: .blarg
 # CHECK: Name: .gnu.warning.foo
 # CHECK: Name: .shstrtab
diff --git a/llvm/test/tools/llvm-objcopy/ELF/strip-non-alloc.test b/llvm/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
--- a/llvm/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
+++ b/llvm/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
@@ -36,8 +36,9 @@
 # RUN: llvm-objcopy --strip-non-alloc %t2 %t2.out
 # RUN: llvm-readobj --file-headers --sections %t2.out | FileCheck --check-prefix=CHECK2 %s
 
-# CHECK2: SectionHeaderCount: 3
+# CHECK2: SectionHeaderCount: 4
 # CHECK2: Name: .text
+# CHECK2: Name: empty_trailing_non_alloc
 # CHECK2: Name: .shstrtab
 
 ---
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
@@ -1057,14 +1057,10 @@
   Visitor.visit(*this);
 }
 
-// Returns true IFF a section is wholly inside the range of a segment
+// Returns true IFF a section is wholly inside the range of a segment. A section
+// can be included by multiple nested segments. If an empty section lies on the
+// boundary between two segments, it will be attributed to both segments.
 static bool sectionWithinSegment(const SectionBase &Sec, const Segment &Seg) {
-  // 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 = Sec.Size ? Sec.Size : 1;
-
   if (Sec.Type == SHT_NOBITS) {
     if (!(Sec.Flags & SHF_ALLOC))
       return false;
@@ -1075,11 +1071,11 @@
       return false;
 
     return Seg.VAddr <= Sec.Addr &&
-           Seg.VAddr + Seg.MemSize >= Sec.Addr + SecSize;
+           Seg.VAddr + Seg.MemSize >= Sec.Addr + Sec.Size;
   }
 
   return Seg.Offset <= Sec.OriginalOffset &&
-         Seg.Offset + Seg.FileSize >= Sec.OriginalOffset + SecSize;
+         Seg.Offset + Seg.FileSize >= Sec.OriginalOffset + Sec.Size;
 }
 
 // Returns true IFF a segment's original offset is inside of another segment's
@@ -1292,7 +1288,7 @@
     for (SectionBase &Sec : Obj.sections())
       if (sectionWithinSegment(Sec, Seg)) {
         Seg.addSection(&Sec);
-        if (!Sec.ParentSegment || Sec.ParentSegment->Offset > Seg.Offset)
+        if (!Sec.ParentSegment || Seg.Offset > Sec.ParentSegment->Offset)
           Sec.ParentSegment = &Seg;
       }
   }