diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
@@ -2468,10 +2468,19 @@
 
 // Fence instruction simplification
 Instruction *InstCombinerImpl::visitFenceInst(FenceInst &FI) {
-  // Remove identical consecutive fences.
   Instruction *Next = FI.getNextNonDebugInstruction();
-  if (auto *NFI = dyn_cast<FenceInst>(Next))
-    if (FI.isIdenticalTo(NFI))
+  if (auto *NFI = dyn_cast<FenceInst>(Next)) {
+    // Remove identical consecutive fences.
+    // When we have a weaker-ordering fence consecutively followed by a
+    // stronger-ordering fence, we can remove the weaker one.
+    if (FI.isIdenticalTo(NFI) || isStrongerThan(NFI->getOrdering(), FI.getOrdering()))
+      return eraseInstFromFunction(FI);
+  }
+
+  // Remove weaker fence if it is preceeded immediately by a stronger ordering
+  // fence.
+  if (auto *PFI = dyn_cast_or_null<FenceInst>(FI.getPrevNonDebugInstruction()))
+    if (isStrongerThan(PFI->getOrdering(), FI.getOrdering()))
       return eraseInstFromFunction(FI);
   return nullptr;
 }
diff --git a/llvm/test/Transforms/InstCombine/consecutive-fences.ll b/llvm/test/Transforms/InstCombine/consecutive-fences.ll
--- a/llvm/test/Transforms/InstCombine/consecutive-fences.ll
+++ b/llvm/test/Transforms/InstCombine/consecutive-fences.ll
@@ -4,7 +4,6 @@
 
 ; CHECK-LABEL: define void @tinkywinky
 ; CHECK-NEXT:   fence seq_cst
-; CHECK-NEXT:   fence syncscope("singlethread") acquire
 ; CHECK-NEXT:   ret void
 ; CHECK-NEXT: }
 
@@ -31,9 +30,6 @@
 }
 
 ; CHECK-LABEL: define void @patatino
-; CHECK-NEXT:   fence acquire
-; CHECK-NEXT:   fence seq_cst
-; CHECK-NEXT:   fence acquire
 ; CHECK-NEXT:   fence seq_cst
 ; CHECK-NEXT:   ret void
 ; CHECK-NEXT: }
@@ -46,6 +42,27 @@
   ret void
 }
 
+; CHECK-LABEL: define void @weaker_fence_1
+; CHECK-NEXT: fence seq_cst
+; CHECK-NEXT: ret void
+define void @weaker_fence_1() {
+  fence seq_cst
+  fence release
+  fence seq_cst
+  ret void
+}
+
+; CHECK-LABEL: define void @weaker_fence_2
+; CHECK-NEXT: fence seq_cst
+; CHECK-NEXT: ret void
+define void @weaker_fence_2() {
+  fence seq_cst
+  fence release
+  fence seq_cst
+  fence acquire 
+  ret void
+}
+
 ; CHECK-LABEL: define void @debug
 ; CHECK-NOT: fence
 ; CHECK: call void @llvm.dbg.value