diff --git a/llvm/lib/Transforms/Utils/FunctionImportUtils.cpp b/llvm/lib/Transforms/Utils/FunctionImportUtils.cpp
--- a/llvm/lib/Transforms/Utils/FunctionImportUtils.cpp
+++ b/llvm/lib/Transforms/Utils/FunctionImportUtils.cpp
@@ -276,7 +276,9 @@
   // When ClearDSOLocalOnDeclarations is true, clear dso_local if GV is
   // converted to a declaration, to disable direct access. Don't do this if GV
   // is implicitly dso_local due to a non-default visibility.
-  if (ClearDSOLocalOnDeclarations && GV.isDeclarationForLinker() &&
+  if (ClearDSOLocalOnDeclarations &&
+      (GV.isDeclarationForLinker() ||
+       (isPerformingImport() && !doImportAsDefinition(&GV))) &&
       !GV.isImplicitDSOLocal()) {
     GV.setDSOLocal(false);
   } else if (VI && VI.isDSOLocal(ImportIndex.withDSOLocalPropagation())) {
diff --git a/llvm/test/ThinLTO/X86/import-dsolocal.ll b/llvm/test/ThinLTO/X86/import-dsolocal.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/ThinLTO/X86/import-dsolocal.ll
@@ -0,0 +1,124 @@
+; RUN: split-file %s %t
+; RUN: opt -module-summary %t/a.ll -o %t/a.bc
+; RUN: opt -module-summary %t/b.ll -o %t/b.bc
+
+;; With a small limit, *_aux are either imported declarations (external/linkonce_odr/weak_odr)
+;; or unimported (linkonce/weak). Check we discard dso_local.
+; RUN: llvm-lto2 run %t/a.bc %t/b.bc -o %t1 -save-temps -import-instr-limit=3 \
+; RUN:   -r=%t/a.bc,main,plx -r=%t/a.bc,extern, -r=%t/a.bc,linkonce, -r=%t/a.bc,linkonceodr, -r=%t/a.bc,weak, -r=%t/a.bc,weakodr, \
+; RUN:   -r=%t/b.bc,a,pl -r=%t/b.bc,b,pl -r=%t/b.bc,extern,pl -r=%t/b.bc,extern_aux,pl \
+; RUN:   -r=%t/b.bc,linkonce,pl -r=%t/b.bc,linkonce_aux,pl -r=%t/b.bc,linkonceodr,pl -r=%t/b.bc,linkonceodr_aux,pl \
+; RUN:   -r=%t/b.bc,weak,pl -r=%t/b.bc,weak_aux,pl -r=%t/b.bc,weakodr,pl -r=%t/b.bc,weakodr_aux,pl
+; RUN: llvm-dis %t1.1.3.import.bc -o - | FileCheck %s --check-prefixes=DEST,DEST1
+
+;; With a large limit, *_aux are either imported definitions (external/linkonce_odr/weak_odr)
+;; or unimported (linkonce/weak). Check we discard dso_local as well.
+; RUN: llvm-lto2 run %t/a.bc %t/b.bc -o %t2 -save-temps -import-instr-limit=10 \
+; RUN:   -r=%t/a.bc,main,plx -r=%t/a.bc,extern, -r=%t/a.bc,linkonce, -r=%t/a.bc,linkonceodr, -r=%t/a.bc,weak, -r=%t/a.bc,weakodr, \
+; RUN:   -r=%t/b.bc,a,pl -r=%t/b.bc,b,pl -r=%t/b.bc,extern,pl -r=%t/b.bc,extern_aux,pl \
+; RUN:   -r=%t/b.bc,linkonce,pl -r=%t/b.bc,linkonce_aux,pl -r=%t/b.bc,linkonceodr,pl -r=%t/b.bc,linkonceodr_aux,pl \
+; RUN:   -r=%t/b.bc,weak,pl -r=%t/b.bc,weak_aux,pl -r=%t/b.bc,weakodr,pl -r=%t/b.bc,weakodr_aux,pl
+; RUN: llvm-dis %t2.1.3.import.bc -o - | FileCheck %s --check-prefixes=DEST,DEST2
+
+; DEST:      @a = available_externally global i32 42, align 4
+; DEST-NEXT: @b = external global i32*, align 8
+; DEST:      declare void @linkonce()
+; DEST:      declare void @weak()
+; DEST:      define dso_local i32 @main()
+; DEST:      define available_externally void @extern()
+
+; DEST1:     declare i32 @extern_aux(i32*, i32**)
+; DEST1:     declare i32 @linkonceodr_aux(i32*, i32**)
+; DEST2:     define available_externally i32 @extern_aux(i32* %a, i32** %b)
+; DEST2:     define available_externally i32 @linkonceodr_aux(i32* %a, i32** %b)
+
+; DEST:      define available_externally void @weakodr()
+
+; DEST1:     declare i32 @weakodr_aux(i32*, i32**)
+; DEST2:     define available_externally i32 @weakodr_aux(i32* %a, i32** %b)
+
+;--- a.ll
+target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+declare void @extern()
+declare void @linkonce()
+declare void @linkonceodr()
+declare void @weak()
+declare void @weakodr()
+
+define i32 @main() {
+  call void @extern()
+  call void @linkonce()
+  call void @linkonceodr()
+  call void @weak()
+  call void @weakodr()
+  ret i32 0
+}
+
+;--- b.ll
+target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+@a = dso_local global i32 42, align 4
+@b = dso_local global i32* @a, align 8
+
+define dso_local void @extern() {
+  call i32 @extern_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define dso_local i32 @extern_aux(i32* %a, i32** %b) {
+  %p = load i32*, i32** %b, align 8
+  store i32 33, i32* %p, align 4
+  %v = load i32, i32* %a, align 4
+  ret i32 %v
+}
+
+define linkonce dso_local void @linkonce() {
+  call i32 @linkonce_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define linkonce i32 @linkonce_aux(i32* %a, i32** %b) {
+  %p = load i32*, i32** %b, align 8
+  store i32 33, i32* %p, align 4
+  %v = load i32, i32* %a, align 4
+  ret i32 %v
+}
+
+define linkonce_odr dso_local void @linkonceodr() {
+  call i32 @linkonceodr_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define linkonce_odr i32 @linkonceodr_aux(i32* %a, i32** %b) {
+  %p = load i32*, i32** %b, align 8
+  store i32 33, i32* %p, align 4
+  %v = load i32, i32* %a, align 4
+  ret i32 %v
+}
+
+define weak dso_local void @weak() {
+  call i32 @weak_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define weak i32 @weak_aux(i32* %a, i32** %b) {
+  %p = load i32*, i32** %b, align 8
+  store i32 33, i32* %p, align 4
+  %v = load i32, i32* %a, align 4
+  ret i32 %v
+}
+
+define weak_odr dso_local void @weakodr() {
+  call i32 @weakodr_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define weak_odr i32 @weakodr_aux(i32* %a, i32** %b) {
+  %p = load i32*, i32** %b, align 8
+  store i32 33, i32* %p, align 4
+  %v = load i32, i32* %a, align 4
+  ret i32 %v
+}
diff --git a/llvm/test/ThinLTO/X86/index-const-prop-linkage.ll b/llvm/test/ThinLTO/X86/index-const-prop-linkage.ll
--- a/llvm/test/ThinLTO/X86/index-const-prop-linkage.ll
+++ b/llvm/test/ThinLTO/X86/index-const-prop-linkage.ll
@@ -10,7 +10,7 @@
 ; - available_externally linkage
 ; - reference from @llvm.used
 ; CHECK:      @llvm.used = appending global [1 x i32*] [i32* @g2]
-; CHECK-NEXT: @g1 = external dso_local global i32, align 4
+; CHECK-NEXT: @g1 = external global i32, align 4
 ; CHECK-NEXT: @g2 = available_externally global i32 42, align 4
 ; CHECK-NEXT: @g3 = available_externally global i32 42, align 4