diff --git a/bolt/include/bolt/Core/BinaryFunction.h b/bolt/include/bolt/Core/BinaryFunction.h
--- a/bolt/include/bolt/Core/BinaryFunction.h
+++ b/bolt/include/bolt/Core/BinaryFunction.h
@@ -2012,7 +2012,9 @@
     return Size;
   }
 
-  bool hasIslandsInfo() const { return !!Islands; }
+  bool hasIslandsInfo() const {
+    return Islands && (hasConstantIsland() || !Islands->Dependency.empty());
+  }
 
   bool hasConstantIsland() const {
     return Islands && !Islands->DataOffsets.empty();
diff --git a/bolt/lib/Core/BinaryFunction.cpp b/bolt/lib/Core/BinaryFunction.cpp
--- a/bolt/lib/Core/BinaryFunction.cpp
+++ b/bolt/lib/Core/BinaryFunction.cpp
@@ -4426,7 +4426,7 @@
 }
 
 bool BinaryFunction::isAArch64Veneer() const {
-  if (empty())
+  if (empty() || hasIslandsInfo())
     return false;
 
   BinaryBasicBlock &BB = **BasicBlocks.begin();
diff --git a/bolt/lib/Passes/IdenticalCodeFolding.cpp b/bolt/lib/Passes/IdenticalCodeFolding.cpp
--- a/bolt/lib/Passes/IdenticalCodeFolding.cpp
+++ b/bolt/lib/Passes/IdenticalCodeFolding.cpp
@@ -162,6 +162,9 @@
   if (A.isMultiEntry() || B.isMultiEntry())
     return false;
 
+  if (A.hasIslandsInfo() || B.hasIslandsInfo())
+    return false;
+
   // Process both functions in either DFS or existing order.
   const BinaryFunction::BasicBlockOrderType OrderA =
       opts::UseDFS
diff --git a/bolt/test/AArch64/prevent-ci-folding.s b/bolt/test/AArch64/prevent-ci-folding.s
new file mode 100644
--- /dev/null
+++ b/bolt/test/AArch64/prevent-ci-folding.s
@@ -0,0 +1,34 @@
+// This test checks that functions containing Constant Islands are not folded even
+// if they have the same data
+
+// RUN: llvm-mc -filetype=obj -triple aarch64-unknown-unknown %s -o %t.o
+// RUN: %clang %cflags --target=aarch64-unknown-linux %t.o -o %t.exe -Wl,-q
+// RUN: llvm-bolt -icf -lite=false %t.exe -o %t.bolt
+// RUN: llvm-objdump -d -j .text %t.bolt | FileCheck %s
+
+// CHECK: <func1>:
+// CHECK: <func2>:
+
+func1:
+    add x0, x0, #1
+    ret
+    .word 0xdeadbeef
+    .word 0xdeadbeef
+.size func1, .-func1
+
+func2:
+    add x0, x0, #1
+    ret
+    .word 0xdeadbeef
+    .word 0xdeadbeef
+.size func2, .-func2
+
+.global        main
+.type  main, %function
+main:
+    mov x0, #0
+    bl     func1
+    bl     func2
+    sub     x0, x0, #2
+    mov     w8, #93
+    svc     #0