diff --git a/llvm/lib/Target/WebAssembly/WebAssemblyISelDAGToDAG.cpp b/llvm/lib/Target/WebAssembly/WebAssemblyISelDAGToDAG.cpp
--- a/llvm/lib/Target/WebAssembly/WebAssemblyISelDAGToDAG.cpp
+++ b/llvm/lib/Target/WebAssembly/WebAssemblyISelDAGToDAG.cpp
@@ -249,8 +249,22 @@
     SmallVector<SDValue, 16> Ops;
     for (size_t i = 1; i < Node->getNumOperands(); ++i) {
       SDValue Op = Node->getOperand(i);
-      if (i == 1 && Op->getOpcode() == WebAssemblyISD::Wrapper)
-        Op = Op->getOperand(0);
+      // Remove the wrapper when the call target is a function, an external
+      // symbol (which will be lowered to a library function), or an alias of
+      // a function. If the target is not a function/external symbol, we
+      // shouldn't remove the wrapper, because we cannot call it directly and
+      // instead we want it to be loaded with a CONST instruction and called
+      // with a call_indirect later.
+      if (i == 1 && Op->getOpcode() == WebAssemblyISD::Wrapper) {
+        SDValue NewOp = Op->getOperand(0);
+        if (auto *GlobalOp = dyn_cast<GlobalAddressSDNode>(NewOp.getNode())) {
+          if (isa<Function>(
+                  GlobalOp->getGlobal()->stripPointerCastsAndAliases()))
+            Op = NewOp;
+        } else if (isa<ExternalSymbolSDNode>(NewOp.getNode())) {
+          Op = NewOp;
+        }
+      }
       Ops.push_back(Op);
     }
 
diff --git a/llvm/test/CodeGen/WebAssembly/call.ll b/llvm/test/CodeGen/WebAssembly/call.ll
--- a/llvm/test/CodeGen/WebAssembly/call.ll
+++ b/llvm/test/CodeGen/WebAssembly/call.ll
@@ -1,5 +1,5 @@
-; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -mattr=+sign-ext,+simd128 | FileCheck --check-prefixes=CHECK,NO-TAIL %s
-; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -fast-isel -fast-isel-abort=1 -mattr=+sign-ext,+simd128 | FileCheck --check-prefixes=CHECK,NO-TAIL %s
+; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -mattr=+sign-ext,+simd128 | FileCheck --check-prefixes=CHECK,SLOW,NO-TAIL %s
+; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -fast-isel -fast-isel-abort=1 -mattr=+sign-ext,+simd128 | FileCheck --check-prefixes=CHECK,FAST,NO-TAIL %s
 ; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -mattr=+sign-ext,+simd128,+tail-call | FileCheck --check-prefixes=CHECK,SLOW-TAIL %s
 ; RUN: llc < %s -asm-verbose=false -disable-wasm-fallthrough-return-opt -wasm-keep-registers -fast-isel -fast-isel-abort=1 -mattr=+sign-ext,+simd128,+tail-call | FileCheck --check-prefixes=CHECK,FAST-TAIL %s
 
@@ -251,6 +251,46 @@
   ret void
 }
 
+; Calling non-functional globals should be lowered to call_indirects.
+; CHECK-LABEL: call_indirect_int:
+; CHECK:      i32.const  $push[[L0:[0-9]+]]=, global_i8
+; CHECK-NEXT: call_indirect  $pop[[L0]]
+; CHECK-NEXT: i32.const  $push[[L1:[0-9]+]]=, global_i32
+; CHECK-NEXT: call_indirect  $pop[[L1]]
+@global_i8 = global i8 0
+@global_i32 = global i32 0
+define void @call_indirect_int() {
+  call void @global_i8()
+  call void @global_i32()
+  ret void
+}
+
+; Calling aliases of non-functional globals should be lowered to call_indirects.
+; CHECK-LABEL: call_indirect_int_alias:
+; CHECK:      i32.const  $push[[L0:[0-9]+]]=, global_i8_alias
+; CHECK-NEXT: call_indirect  $pop[[L0]]
+; CHECK-NEXT: i32.const  $push[[L1:[0-9]+]]=, global_i32_alias
+; CHECK-NEXT: call_indirect  $pop[[L1]]
+@global_i8_alias = alias i8, ptr @global_i8
+@global_i32_alias = alias i32, ptr @global_i32
+define void @call_indirect_int_alias() {
+  call void @global_i8_alias()
+  call void @global_i32_alias()
+  ret void
+}
+
+; Ideally calling aliases of functions should be lowered to direct calls. We
+; support this in the normal (=slow) isel.
+; CHECK-LABEL: call_func_alias:
+; SLOW:      call  func_alias
+; FAST:      i32.const  $push[[L0:[0-9]+]]=, func_alias
+; FAST-NEXT: call_indirect  $pop[[L0]]
+@func_alias = alias void (), ptr @call_void_nullary
+define void @call_func_alias() {
+  call void @func_alias()
+  ret void
+}
+
 ; TODO: test the following:
 ;  - More argument combinations.
 ;  - Tail call.