diff --git a/bolt/lib/Passes/VeneerElimination.cpp b/bolt/lib/Passes/VeneerElimination.cpp
index b386b2756a2b8..99d0ffeca8cc2 100644
--- a/bolt/lib/Passes/VeneerElimination.cpp
+++ b/bolt/lib/Passes/VeneerElimination.cpp
@@ -46,16 +46,17 @@ Error VeneerElimination::runOnFunctions(BinaryContext &BC) {
     if (BF.isIgnored())
       continue;
 
+    MCInst &FirstInstruction = *(BF.begin()->begin());
     const MCSymbol *VeneerTargetSymbol = 0;
     uint64_t TargetAddress;
-    if (BC.MIB->matchAbsLongVeneer(BF, TargetAddress)) {
+    if (BC.MIB->isTailCall(FirstInstruction)) {
+      VeneerTargetSymbol = BC.MIB->getTargetSymbol(FirstInstruction);
+    } else if (BC.MIB->matchAbsLongVeneer(BF, TargetAddress)) {
       if (BinaryFunction *TargetBF =
               BC.getBinaryFunctionAtAddress(TargetAddress))
         VeneerTargetSymbol = TargetBF->getSymbol();
-    } else {
-      MCInst &FirstInstruction = *(BF.begin()->begin());
-      if (BC.MIB->hasAnnotation(FirstInstruction, "AArch64Veneer"))
-        VeneerTargetSymbol = BC.MIB->getTargetSymbol(FirstInstruction, 1);
+    } else if (BC.MIB->hasAnnotation(FirstInstruction, "AArch64Veneer")) {
+      VeneerTargetSymbol = BC.MIB->getTargetSymbol(FirstInstruction, 1);
     }
 
     if (!VeneerTargetSymbol)
diff --git a/bolt/test/AArch64/veneer-lld-abs.s b/bolt/test/AArch64/veneer-lld-abs.s
index d10ff46e2cb01..7e6fe2d127060 100644
--- a/bolt/test/AArch64/veneer-lld-abs.s
+++ b/bolt/test/AArch64/veneer-lld-abs.s
@@ -1,5 +1,5 @@
-## Check that llvm-bolt correctly recognizes long absolute thunks generated
-## by LLD.
+## Check that llvm-bolt correctly recognizes veneers/thunks for absolute code
+## generated by LLD.
 
 # RUN: llvm-mc -filetype=obj -triple aarch64-unknown-unknown %s -o %t.o
 # RUN: %clang %cflags -fno-PIC -no-pie %t.o -o %t.exe -nostdlib \
@@ -12,40 +12,63 @@
 
 .text
 .balign 4
-.global foo
-.type foo, %function
-foo:
-  adrp x1, foo
+.global far_function
+.type far_function, %function
+far_function:
   ret
-.size foo, .-foo
+.size far_function, .-far_function
+
+.global near_function
+.type near_function, %function
+near_function:
+  ret
+.size near_function, .-near_function
+
+## Force relocations against .text.
+.reloc 0, R_AARCH64_NONE
 
 .section ".mytext", "ax"
 .balign 4
 
-.global __AArch64AbsLongThunk_foo
-.type __AArch64AbsLongThunk_foo, %function
-__AArch64AbsLongThunk_foo:
+## This version of a thunk is always generated by LLD for function calls
+## spanning more than 256MB.
+.global __AArch64AbsLongThunk_far_function
+.type __AArch64AbsLongThunk_far_function, %function
+__AArch64AbsLongThunk_far_function:
   ldr x16, .L1
   br x16
-# CHECK-INPUT-LABEL: <__AArch64AbsLongThunk_foo>:
+# CHECK-INPUT-LABEL: <__AArch64AbsLongThunk_far_function>:
 # CHECK-INPUT-NEXT:    ldr
 # CHECK-INPUT-NEXT:    br
 .L1:
-  .quad foo
-.size __AArch64AbsLongThunk_foo, .-__AArch64AbsLongThunk_foo
+  .quad far_function
+.size __AArch64AbsLongThunk_far_function, .-__AArch64AbsLongThunk_far_function
+
+## If a callee is closer than 256MB away, LLD may generate a thunk with a direct
+## jump to the callee. Note, that the name might still include "AbsLong".
+.global __AArch64AbsLongThunk_near_function
+.type __AArch64AbsLongThunk_near_function, %function
+__AArch64AbsLongThunk_near_function:
+  b near_function
+# CHECK-INPUT-LABEL: <__AArch64AbsLongThunk_near_function>:
+# CHECK-INPUT-NEXT:    b {{.*}} <near_function>
+.size __AArch64AbsLongThunk_near_function, .-__AArch64AbsLongThunk_near_function
 
-## Check that the thunk was removed from .text and _start() calls foo()
+## Check that thunks were removed from .text, and _start calls functions
 ## directly.
 
-# CHECK-OUTPUT-NOT: __AArch64AbsLongThunk_foo
+# CHECK-OUTPUT-NOT: __AArch64AbsLongThunk_{{.*}}
 
 .global _start
 .type _start, %function
 _start:
 # CHECK-INPUT-LABEL:  <_start>:
 # CHECK-OUTPUT-LABEL: <_start>:
-  bl __AArch64AbsLongThunk_foo
-# CHECK-INPUT-NEXT:     bl {{.*}} <__AArch64AbsLongThunk_foo>
-# CHECK-OUTPUT-NEXT:    bl {{.*}} <foo>
+  bl __AArch64AbsLongThunk_far_function
+  bl __AArch64AbsLongThunk_near_function
+# CHECK-INPUT-NEXT:     bl {{.*}} <__AArch64AbsLongThunk_far_function>
+# CHECK-INPUT-NEXT:     bl {{.*}} <__AArch64AbsLongThunk_near_function>
+# CHECK-OUTPUT-NEXT:    bl {{.*}} <far_function>
+# CHECK-OUTPUT-NEXT:    bl {{.*}} <near_function>
   ret
 .size _start, .-_start