diff --git a/Eigen/src/Core/products/CoeffBasedProduct.h b/Eigen/src/Core/products/CoeffBasedProduct.h
--- a/Eigen/src/Core/products/CoeffBasedProduct.h
+++ b/Eigen/src/Core/products/CoeffBasedProduct.h
@@ -80,17 +80,18 @@ struct traits<CoeffBasedProduct<LhsNeste
 
       EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
                      : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
                      : (RhsRowMajor && !CanVectorizeLhs),
 
       Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & ~RowMajorBit)
             | (EvalToRowMajor ? RowMajorBit : 0)
             | NestingFlags
-            | (LhsFlags & RhsFlags & AlignedBit)
+            | (CanVectorizeLhs ? (LhsFlags & AlignedBit) : 0)
+            | (CanVectorizeRhs ? (RhsFlags & AlignedBit) : 0)
             // TODO enable vectorization for mixed types
             | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0),
 
       CoeffReadCost = InnerSize == Dynamic ? Dynamic
                     : InnerSize * (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
                       + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
 
       /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside