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
@@ -115,16 +115,22 @@
     return SGV->getLinkage();
 
   switch (SGV->getLinkage()) {
-  case GlobalValue::LinkOnceODRLinkage:
   case GlobalValue::ExternalLinkage:
-    // External and linkonce definitions are converted to available_externally
-    // definitions upon import, so that they are available for inlining
-    // and/or optimization, but are turned into declarations later
+  case GlobalValue::LinkOnceODRLinkage:
+  case GlobalValue::WeakODRLinkage:
+    // External and linkonce_odr definitions are converted to
+    // available_externally definitions upon import, so that they are available
+    // for inlining and/or optimization, but are turned into declarations later
     // during the EliminateAvailableExternally pass.
-    if (doImportAsDefinition(SGV) && !isa<GlobalAlias>(SGV))
+    //
+    // For weak_odr linkage, there is a guarantee that all copies will be
+    // equivalent, so the issue described below for weak_any does not exist,
+    // and the definition can be imported. It can be treated similarly
+    // to an imported externally visible global value.
+    if (!SGV->isDeclarationForLinker() && !isa<GlobalAlias>(SGV))
       return GlobalValue::AvailableExternallyLinkage;
     // An imported external declaration stays external.
-    return SGV->getLinkage();
+    return GlobalValue::ExternalLinkage;
 
   case GlobalValue::AvailableExternallyLinkage:
     // An imported available_externally definition converts
@@ -145,16 +151,6 @@
     // If imported as a declaration, it becomes external_weak.
     return SGV->getLinkage();
 
-  case GlobalValue::WeakODRLinkage:
-    // For weak_odr linkage, there is a guarantee that all copies will be
-    // equivalent, so the issue described above for weak_any does not exist,
-    // and the definition can be imported. It can be treated similarly
-    // to an imported externally visible global value.
-    if (doImportAsDefinition(SGV) && !isa<GlobalAlias>(SGV))
-      return GlobalValue::AvailableExternallyLinkage;
-    else
-      return GlobalValue::ExternalLinkage;
-
   case GlobalValue::AppendingLinkage:
     // It would be incorrect to import an appending linkage variable,
     // since it would cause global constructors/destructors to be
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 +1,85 @@
+; 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 not imported. 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,linkonceodr, -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,linkonceodr,pl -r=%t/b.bc,linkonceodr_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 imported. Check we still discard dso_local.
+; 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,linkonceodr, -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,linkonceodr,pl -r=%t/b.bc,linkonceodr_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:      define dso_local i32 @main()
+; DEST:      define available_externally void @extern()
+; DEST1:     declare i32 @extern_aux(i32*, i32**)
+; DEST2:     define available_externally i32 @extern_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 @linkonceodr()
+declare void @weakodr()
+
+define i32 @main() {
+  call void @extern()
+  call void @linkonceodr()
+  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 weak_odr dso_local void @linkonceodr() {
+  call i32 @linkonceodr_aux(i32* @a, i32** @b)
+  ret void
+}
+
+define weak_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_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
+}