diff --git a/src/coreclr/jit/gentree.h b/src/coreclr/jit/gentree.h
index e55073378cddd9..f3f87ed8110da7 100644
--- a/src/coreclr/jit/gentree.h
+++ b/src/coreclr/jit/gentree.h
@@ -3337,6 +3337,7 @@ struct GenTreeIntConCommon : public GenTree
     inline ssize_t IconValue() const;
     inline void    SetIconValue(ssize_t val);
     inline INT64   IntegralValue() const;
+    inline UINT64  UnsignedIntegralValue() const;
     inline void    SetIntegralValue(int64_t value);
 
     template <typename T>
@@ -3540,6 +3541,13 @@ inline INT64 GenTreeIntConCommon::IntegralValue() const
 #endif // TARGET_64BIT
 }
 
+inline UINT64 GenTreeIntConCommon::UnsignedIntegralValue() const
+{
+    INT64  signExtended = IntegralValue();
+    UINT64 zeroExtended = TypeIs(TYP_LONG) ? signExtended : (uint32_t)signExtended;
+    return zeroExtended;
+}
+
 inline void GenTreeIntConCommon::SetIntegralValue(int64_t value)
 {
 #ifdef TARGET_64BIT
diff --git a/src/coreclr/jit/morph.cpp b/src/coreclr/jit/morph.cpp
index 7caba07734be6d..bcec7a85d7c9ff 100644
--- a/src/coreclr/jit/morph.cpp
+++ b/src/coreclr/jit/morph.cpp
@@ -7768,6 +7768,17 @@ GenTree* Compiler::fgMorphSmpOp(GenTree* tree, MorphAddrContext* mac, bool* optA
 
         case GT_EQ:
         case GT_NE:
+            // Change "CNS relop op2" to "op2 relop* CNS"
+            if (op1->IsIntegralConst() && tree->OperIsCompare() && gtCanSwapOrder(op1, op2))
+            {
+                std::swap(tree->AsOp()->gtOp1, tree->AsOp()->gtOp2);
+                tree->gtOper = GenTree::SwapRelop(tree->OperGet());
+
+                oper = tree->OperGet();
+                op1  = tree->gtGetOp1();
+                op2  = tree->gtGetOp2();
+            }
+
             if (op2->IsIntegralConst())
             {
                 tree = fgOptimizeEqualityComparisonWithConst(tree->AsOp());
@@ -8748,6 +8759,20 @@ GenTree* Compiler::fgOptimizeEqualityComparisonWithConst(GenTreeOp* cmp)
     GenTree*             op1 = cmp->gtGetOp1();
     GenTreeIntConCommon* op2 = cmp->gtGetOp2()->AsIntConCommon();
 
+    // Canonicalize
+    // '(A & pow2) == pow2' -> '(A & pow2) != 0'
+    // '(A & pow2) != pow2' -> '(A & pow2) == 0'
+    if (op1->OperIs(GT_AND) && op1->gtGetOp2()->IsIntegralConst())
+    {
+        if (BitOperations::PopCount(op2->UnsignedIntegralValue()) == 1 &&
+            (op1->gtGetOp2()->AsIntConCommon()->IntegralValue() == op2->IntegralValue()))
+        {
+            cmp->SetOper(cmp->OperIs(GT_EQ) ? GT_NE : GT_EQ, GenTree::PRESERVE_VN);
+            op2->SetIntegralValue(0);
+            fgUpdateConstTreeValueNumber(op2);
+        }
+    }
+
     // Fold: (-(x)) == 0  ->  x == 0  (avoid neg on compare-to-zero)
     if (op1->OperIs(GT_NEG) && !op1->gtOverflowEx())
     {