diff --git a/test/tools/llvm-objcopy/ELF/remove-section-in-segment.test b/test/tools/llvm-objcopy/ELF/remove-section-in-segment.test
new file mode 100644
index 0000000..036c954
--- /dev/null
+++ b/test/tools/llvm-objcopy/ELF/remove-section-in-segment.test
@@ -0,0 +1,47 @@
+# Show that --remove-section removes sections in segments.
+
+# RUN: yaml2obj %s -o %t
+
+# Validate the offsets for the later parts of the test.
+# RUN: llvm-objcopy %t %t.copy
+# Skip to the start of the sections, which should be immediately after the
+# program header table (i.e. sizeof(Elf64_Ehdr) + sizeof(Elf64_Phdr) == 120).
+# RUN: od -t x1 -N 16 -j 120 %t.copy | FileCheck %s --check-prefix=COPY
+
+# COPY: 11 22 33 44 55 66 77 88
+
+# RUN: llvm-objcopy --remove-section non_alloc %t %t.nonalloc
+# RUN: llvm-readelf --sections %t.nonalloc | FileCheck %s --check-prefix=NONALLOC-SHDRS
+# RUN: od -t x1 -N 16 -j 120 %t.nonalloc | FileCheck %s --check-prefix=NONALLOC-BYTES
+
+# NONALLOC-SHDRS-NOT: non_alloc
+# NONALLOC-BYTES: 11 22 33 44 00 00 00 00
+
+# RUN: llvm-objcopy --remove-section shf_alloc %t %t.alloc
+# RUN: llvm-readelf --sections %t.alloc | FileCheck %s --check-prefix=ALLOC-SHDRS
+# RUN: od -t x1 -N 16 -j 120 %t.alloc | FileCheck %s --check-prefix=ALLOC-BYTES
+
+# ALLOC-SHDRS-NOT: shf_alloc
+# ALLOC-BYTES: 00 00 00 00 55 66 77 88
+
+--- !ELF
+FileHeader:
+  Class:   ELFCLASS64
+  Data:    ELFDATA2LSB
+  Type:    ET_EXEC
+  Machine: EM_X86_64
+Sections:
+  - Name:    shf_alloc
+    Type:    SHT_PROGBITS
+    Flags:   [SHF_ALLOC]
+    Content: '11223344'
+  - Name:    non_alloc
+    Type:    SHT_PROGBITS
+    Flags:   []
+    Content: '55667788'
+ProgramHeaders:
+  # Use an arbitrary segment type to show that the segment type is unimportant.
+  - Type: 0x61234567
+    Sections:
+      - Section: shf_alloc
+      - Section: non_alloc
diff --git a/test/tools/llvm-objcopy/ELF/strip-all-gnu.test b/test/tools/llvm-objcopy/ELF/strip-all-gnu.test
index 8253526..ea2cb63 100644
--- a/test/tools/llvm-objcopy/ELF/strip-all-gnu.test
+++ b/test/tools/llvm-objcopy/ELF/strip-all-gnu.test
@@ -1,10 +1,15 @@
 # RUN: yaml2obj %s > %t
-# RUN: cp %t %t1
 # RUN: llvm-objcopy --strip-all-gnu %t %t2
 # RUN: llvm-strip --strip-all-gnu %t -o %t3
 # RUN: llvm-readobj --file-headers --sections %t2 | FileCheck %s
 # RUN: cmp %t2 %t3
 
+# Show that the debug section in a segment was removed, to match GNU.
+# First validate that the offset in use is correct.
+# RUN: llvm-objcopy %t %t4
+# RUN: od -t x1 -N 4 -j 120 %t4 | FileCheck %s --check-prefix=COPY-BYTES
+# RUN: od -t x1 -N 4 -j 120 %t2 | FileCheck %s --check-prefix=STRIP-BYTES
+
 !ELF
 FileHeader:
   Class:           ELFCLASS64
@@ -12,6 +17,10 @@
   Type:            ET_REL
   Machine:         EM_X86_64
 Sections:
+  - Name:            .debug_in_segment
+    Type:            SHT_PROGBITS
+    Flags:           [ ]
+    Content:         "deadbeef"
   - Name:            .dynstr
     Type:            SHT_STRTAB
     Flags:           [ SHF_ALLOC ]
@@ -45,6 +54,11 @@
   - Name:            .rela.text
     Type:            SHT_RELA
     Info:            .text
+ProgramHeaders:
+  # Use an arbitrary segment type to show that the segment type is unimportant.
+  - Type: 0x61234567
+    Sections:
+      - Section: .debug_in_segment
 
 # CHECK: SectionHeaderCount: 8
 
@@ -55,3 +69,6 @@
 # CHECK:      Name: .comment
 # CHECK:      Name: .random_section_name
 # CHECK:      Name: .shstrtab
+
+# COPY-BYTES:  de ad be ef
+# STRIP-BYTES: 00 00 00 00
diff --git a/test/tools/llvm-objcopy/ELF/strip-all.test b/test/tools/llvm-objcopy/ELF/strip-all.test
index 87388e0..32a801d 100644
--- a/test/tools/llvm-objcopy/ELF/strip-all.test
+++ b/test/tools/llvm-objcopy/ELF/strip-all.test
@@ -57,6 +57,10 @@
   Type:            ET_REL
   Machine:         EM_X86_64
 Sections:
+  - Name:            non_alloc_in_segment
+    Type:            SHT_PROGBITS
+    Flags:           [ ]
+    Size:            4
   - Name:            .bss
     Type:            SHT_NOBITS
     Flags:           [ SHF_ALLOC ]
@@ -68,9 +72,15 @@
     Flags:           [ ]
   - Name:            .gnu.warning.foo
     Type:            SHT_PROGBITS
+ProgramHeaders:
+  # Use an arbitrary segment type to show that the segment type is unimportant.
+  - Type: 0x61234567
+    Sections:
+      - Section: non_alloc_in_segment
 
-# CHECK: SectionHeaderCount: 5
+# CHECK: SectionHeaderCount: 6
 
+# CHECK: Name: non_alloc_in_segment
 # CHECK: Name: .bss
 # CHECK: Name: .text
 # CHECK: Name: .gnu.warning.foo
diff --git a/test/tools/llvm-objcopy/ELF/strip-non-alloc.test b/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
index 8db7321..1f082bf 100644
--- a/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
+++ b/test/tools/llvm-objcopy/ELF/strip-non-alloc.test
@@ -9,6 +9,10 @@
   Type:            ET_REL
   Machine:         EM_X86_64
 Sections:
+  - Name:            non_alloc_in_segment
+    Type:            SHT_PROGBITS
+    Flags:           [ ]
+    Size:            4
   - Name:            .bss
     Type:            SHT_NOBITS
     Flags:           [ SHF_ALLOC ]
@@ -18,9 +22,15 @@
   - Name:            .blarg
     Type:            SHT_PROGBITS
     Flags:           [ ]
+ProgramHeaders:
+  # Use an arbitrary segment type to show that the segment type is unimportant.
+  - Type: 0x61234567
+    Sections:
+      - Section: non_alloc_in_segment
 
-# CHECK: SectionHeaderCount: 4
+# CHECK: SectionHeaderCount: 5
 
+# CHECK: Name: non_alloc_in_segment
 # CHECK: Name: .bss
 # CHECK: Name: .text
 # CHECK: Name: .shstrtab
diff --git a/test/tools/llvm-objcopy/ELF/strip-sections.test b/test/tools/llvm-objcopy/ELF/strip-sections.test
index 2dee6e2..244cdb3 100644
--- a/test/tools/llvm-objcopy/ELF/strip-sections.test
+++ b/test/tools/llvm-objcopy/ELF/strip-sections.test
@@ -15,13 +15,18 @@
     Flags:           [ SHF_ALLOC, SHF_EXECINSTR ]
     AddressAlign:    0x0000000000001000
     Content:         "DEADBEEF"
+  - Name:            .non_alloc_in_segment
+    Type:            SHT_PROGBITS
+    Flags:           [ ]
+    Content:         "CAFEBABE"
 ProgramHeaders:
 - Type: PT_LOAD
   Flags: [ PF_X, PF_R ]
   Sections:
     - Section: .text
+    - Section: .non_alloc_in_segment
 
-#DATA: 0010000 de ad be ef
+#DATA: 0010000 de ad be ef ca fe ba be
 
 #CHECK: ElfHeader {
 #CHECK-NEXT:  Ident {
@@ -55,8 +60,8 @@
 #CHECK-NEXT:    Offset: 0x1000
 #CHECK-NEXT:    VirtualAddress: 0x0
 #CHECK-NEXT:    PhysicalAddress: 0x0
-#CHECK-NEXT:    FileSize: 4
-#CHECK-NEXT:    MemSize: 4
+#CHECK-NEXT:    FileSize: 8
+#CHECK-NEXT:    MemSize: 8
 #CHECK-NEXT:    Flags [ (0x5)
 #CHECK-NEXT:      PF_R (0x4)
 #CHECK-NEXT:      PF_X (0x1)
diff --git a/tools/llvm-objcopy/ELF/ELFObjcopy.cpp b/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
index cbf6a3d..250eeea 100644
--- a/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
+++ b/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
@@ -403,7 +403,7 @@
 
   if (Config.StripSections) {
     RemovePred = [RemovePred](const SectionBase &Sec) {
-      return RemovePred(Sec) || (Sec.Flags & SHF_ALLOC) == 0;
+      return RemovePred(Sec) || Sec.ParentSegment == nullptr;
     };
   }
 
@@ -419,7 +419,7 @@
         return true;
       if (&Sec == Obj.SectionNames)
         return false;
-      return (Sec.Flags & SHF_ALLOC) == 0;
+      return (Sec.Flags & SHF_ALLOC) == 0 && Sec.ParentSegment == nullptr;
     };
 
   if (Config.StripAll)
@@ -430,6 +430,8 @@
         return false;
       if (StringRef(Sec.Name).startswith(".gnu.warning"))
         return false;
+      if (Sec.ParentSegment != nullptr)
+        return false;
       return (Sec.Flags & SHF_ALLOC) == 0;
     };
 
diff --git a/tools/llvm-objcopy/ObjcopyOpts.td b/tools/llvm-objcopy/ObjcopyOpts.td
index 44fd01c..a5f7119 100644
--- a/tools/llvm-objcopy/ObjcopyOpts.td
+++ b/tools/llvm-objcopy/ObjcopyOpts.td
@@ -103,10 +103,9 @@
          "rom, share, contents, merge, strings.">,
       MetaVarName<"section=flag1[,flag2,...]">;
 
-def strip_all
-    : Flag<["-", "--"], "strip-all">,
-      HelpText<
-          "Remove non-allocated sections other than .gnu.warning* sections">;
+def strip_all : Flag<["-", "--"], "strip-all">,
+                HelpText<"Remove non-allocated sections outside segments. "
+                         ".gnu.warning* sections are not removed">;
 def S : Flag<["-"], "S">, Alias<strip_all>;
 def strip_all_gnu : Flag<["-", "--"], "strip-all-gnu">,
                     HelpText<"Compatible with GNU objcopy's --strip-all">;
@@ -116,13 +115,15 @@
         HelpText<"Alias for --strip-debug">;
 def strip_dwo : Flag<["-", "--"], "strip-dwo">,
                 HelpText<"Remove all DWARF .dwo sections from file">;
-def strip_sections : Flag<["-", "--"], "strip-sections">,
-                     HelpText<"Remove all section headers">;
-def strip_non_alloc : Flag<["-", "--"], "strip-non-alloc">,
-                      HelpText<"Remove all non-allocated sections">;
+def strip_sections
+    : Flag<["-", "--"], "strip-sections">,
+      HelpText<"Remove all section headers and all sections not in segments">;
+def strip_non_alloc
+    : Flag<["-", "--"], "strip-non-alloc">,
+      HelpText<"Remove all non-allocated sections outside segments">;
 def strip_unneeded : Flag<["-", "--"], "strip-unneeded">,
                      HelpText<"Remove all symbols not needed by relocations">;
-defm strip_unneeded_symbol 
+defm strip_unneeded_symbol
     : Eq<"strip-unneeded-symbol",
          "Remove symbol <symbol> if it is not needed by relocations">,
       MetaVarName<"symbol">;
diff --git a/tools/llvm-objcopy/StripOpts.td b/tools/llvm-objcopy/StripOpts.td
index c3f3519..40b043a 100644
--- a/tools/llvm-objcopy/StripOpts.td
+++ b/tools/llvm-objcopy/StripOpts.td
@@ -31,10 +31,9 @@
                      HelpText<"Preserve access and modification timestamps">;
 def p : Flag<["-"], "p">, Alias<preserve_dates>;
 
-def strip_all
-    : Flag<["-", "--"], "strip-all">,
-      HelpText<
-          "Remove non-allocated sections other than .gnu.warning* sections">;
+def strip_all : Flag<["-", "--"], "strip-all">,
+                HelpText<"Remove non-allocated sections outside segments. "
+                         ".gnu.warning* sections are not removed">;
 def s : Flag<["-"], "s">, Alias<strip_all>;
 
 def strip_all_gnu : Flag<["-", "--"], "strip-all-gnu">,