diff --git a/Eigen/src/Core/AssignEvaluator.h b/Eigen/src/Core/AssignEvaluator.h
index 39efb1d5a..f589555cc 100644
--- a/Eigen/src/Core/AssignEvaluator.h
+++ b/Eigen/src/Core/AssignEvaluator.h
@@ -365,13 +365,14 @@ struct dense_assignment_loop<Kernel, LinearVectorizedTraversal, NoUnrolling>
     typedef typename Kernel::Scalar Scalar;
     typedef packet_traits<Scalar> PacketTraits;
     enum {
+      requestedAlignment = Kernel::AssignmentTraits::RequiredAlignment,
       packetSize = PacketTraits::size,
-      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(Kernel::AssignmentTraits::RequiredAlignment),
-      dstAlignment = PacketTraits::AlignedOnScalar ? int(Kernel::AssignmentTraits::RequiredAlignment)
+      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),
+      dstAlignment = PacketTraits::AlignedOnScalar ? int(requestedAlignment)
                                                    : int(Kernel::AssignmentTraits::DstAlignment),
       srcAlignment = Kernel::AssignmentTraits::JointAlignment
     };
-    const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned(&kernel.dstEvaluator().coeffRef(0), size);
+    const Index alignedStart = dstIsAligned ? 0 : internal::first_aligned<requestedAlignment>(&kernel.dstEvaluator().coeffRef(0), size);
     const Index alignedEnd = alignedStart + ((size-alignedStart)/packetSize)*packetSize;
 
     unaligned_dense_assignment_loop<dstIsAligned!=0>::run(kernel, 0, alignedStart);
@@ -479,9 +480,10 @@ struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, NoUnrolling>
     typedef packet_traits<Scalar> PacketTraits;
     enum {
       packetSize = PacketTraits::size,
+      requestedAlignment = int(Kernel::AssignmentTraits::RequiredAlignment),
       alignable = PacketTraits::AlignedOnScalar || int(Kernel::AssignmentTraits::DstAlignment)>=sizeof(Scalar),
-      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(Kernel::AssignmentTraits::RequiredAlignment),
-      dstAlignment = alignable ? int(Kernel::AssignmentTraits::RequiredAlignment)
+      dstIsAligned = int(Kernel::AssignmentTraits::DstAlignment)>=int(requestedAlignment),
+      dstAlignment = alignable ? int(requestedAlignment)
                                : int(Kernel::AssignmentTraits::DstAlignment)
     };
     const Scalar *dst_ptr = &kernel.dstEvaluator().coeffRef(0,0);
@@ -494,7 +496,7 @@ struct dense_assignment_loop<Kernel, SliceVectorizedTraversal, NoUnrolling>
     const Index innerSize = kernel.innerSize();
     const Index outerSize = kernel.outerSize();
     const Index alignedStep = alignable ? (packetSize - kernel.outerStride() % packetSize) & packetAlignedMask : 0;
-    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned(dst_ptr, innerSize);
+    Index alignedStart = ((!alignable) || bool(dstIsAligned)) ? 0 : internal::first_aligned<requestedAlignment>(dst_ptr, innerSize);
 
     for(Index outer = 0; outer < outerSize; ++outer)
     {
diff --git a/Eigen/src/Core/DenseCoeffsBase.h b/Eigen/src/Core/DenseCoeffsBase.h
index 11e2a1809..d053911e3 100644
--- a/Eigen/src/Core/DenseCoeffsBase.h
+++ b/Eigen/src/Core/DenseCoeffsBase.h
@@ -580,33 +580,41 @@ class DenseCoeffsBase<Derived, DirectWriteAccessors>
 
 namespace internal {
 
-template<typename Derived, bool JustReturnZero>
+template<int Alignment, typename Derived, bool JustReturnZero>
 struct first_aligned_impl
 {
   static inline Index run(const Derived&)
   { return 0; }
 };
 
-template<typename Derived>
-struct first_aligned_impl<Derived, false>
+template<int Alignment, typename Derived>
+struct first_aligned_impl<Alignment, Derived, false>
 {
   static inline Index run(const Derived& m)
   {
-    return internal::first_aligned(&m.const_cast_derived().coeffRef(0,0), m.size());
+    return internal::first_aligned<Alignment>(&m.const_cast_derived().coeffRef(0,0), m.size());
   }
 };
 
-/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
+/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization.
+  *
+  * \tparam Alignment requested alignment in Bytes.
   *
   * There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
   * documentation.
   */
-template<typename Derived>
+template<int Alignment, typename Derived>
 static inline Index first_aligned(const DenseBase<Derived>& m)
 {
-  return first_aligned_impl
-          <Derived, (evaluator<Derived>::Alignment > 0 ) || !(Derived::Flags & DirectAccessBit)> // FIXME Alignment!
-          ::run(m.derived());
+  enum { ReturnZero = (int(evaluator<Derived>::Alignment) >= Alignment) || !(Derived::Flags & DirectAccessBit) };
+  return first_aligned_impl<Alignment, Derived, ReturnZero>::run(m.derived());
+}
+
+template<typename Derived>
+static inline Index first_default_aligned(const DenseBase<Derived>& m)
+{
+  typedef typename Derived::Scalar Scalar;
+  return first_aligned<packet_traits<Scalar>::size*sizeof(Scalar)>(m);
 }
 
 template<typename Derived, bool HasDirectAccess = has_direct_access<Derived>::ret>
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index 0c25223aa..fa308b53e 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -221,12 +221,13 @@ struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
   {
     const Index size = mat.size();
     
-    const Index packetSize = packet_traits<Scalar>::size;
-    const Index alignedStart = internal::first_aligned(mat.nestedExpression());
+    const Index packetSize  = packet_traits<Scalar>::size;
+    const int packetBytes = int(packetSize*sizeof(Scalar));
     enum {
-      alignment0 = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(sizeof(Scalar)*packetSize) : int(Unaligned), // FIXME take into account alignment requirement
+      alignment0 = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetBytes) : int(Unaligned), // FIXME take into account alignment requirement
       alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Derived::Alignment)
     };
+    const Index alignedStart = internal::first_default_aligned(mat.nestedExpression());
     const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
     const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
     const Index alignedEnd2 = alignedStart + alignedSize2;
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
index aca81f463..7fe39808b 100644
--- a/Eigen/src/Core/StableNorm.h
+++ b/Eigen/src/Core/StableNorm.h
@@ -178,7 +178,7 @@ MatrixBase<Derived>::stableNorm() const
   if(n==1)
     return abs(this->coeff(0));
   
-  Index bi = internal::first_aligned(copy);
+  Index bi = internal::first_default_aligned(copy);
   if (bi>0)
     internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);
   for (; bi<n; bi+=blockSize)
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
index 439f14456..8b7dca45f 100644
--- a/Eigen/src/Core/products/GeneralMatrixVector.h
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -125,7 +125,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,LhsMapper,C
 
   // How many coeffs of the result do we have to skip to be aligned.
   // Here we assume data are at least aligned on the base scalar type.
-  Index alignedStart = internal::first_aligned(res,size);
+  Index alignedStart = internal::first_default_aligned(res,size);
   Index alignedSize = ResPacketSize>1 ? alignedStart + ((size-alignedStart) & ~ResPacketAlignedMask) : 0;
   const Index peeledSize = alignedSize - RhsPacketSize*peels - RhsPacketSize + 1;
 
diff --git a/Eigen/src/Core/products/SelfadjointMatrixVector.h b/Eigen/src/Core/products/SelfadjointMatrixVector.h
index 5d6ef9913..f3443bd10 100644
--- a/Eigen/src/Core/products/SelfadjointMatrixVector.h
+++ b/Eigen/src/Core/products/SelfadjointMatrixVector.h
@@ -94,7 +94,7 @@ EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrd
 
     size_t starti = FirstTriangular ? 0 : j+2;
     size_t endi   = FirstTriangular ? j : size;
-    size_t alignedStart = (starti) + internal::first_aligned(&res[starti], endi-starti);
+    size_t alignedStart = (starti) + internal::first_default_aligned(&res[starti], endi-starti);
     size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
 
     // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix.h b/Eigen/src/Core/products/TriangularMatrixMatrix.h
index 3d2345b66..39ab87df8 100644
--- a/Eigen/src/Core/products/TriangularMatrixMatrix.h
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix.h
@@ -257,6 +257,7 @@ EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
     Scalar* _res,        Index resStride,
     const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
   {
+    const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar);
     // strip zeros
     Index diagSize  = (std::min)(_cols,_depth);
     Index rows      = _rows;
@@ -311,7 +312,7 @@ EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
       Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
 
       Scalar* geb = blockB+ts*ts;
-      geb = geb + internal::first_aligned(geb,EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar));
+      geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar));
 
       pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs);
 
diff --git a/Eigen/src/Core/util/BlasUtil.h b/Eigen/src/Core/util/BlasUtil.h
index 934948ebd..d00fa9707 100755
--- a/Eigen/src/Core/util/BlasUtil.h
+++ b/Eigen/src/Core/util/BlasUtil.h
@@ -230,7 +230,7 @@ class blas_data_mapper {
     if (size_t(m_data)%sizeof(Scalar)) {
       return -1;
     }
-    return internal::first_aligned(m_data, size);
+    return internal::first_default_aligned(m_data, size);
   }
 
   protected:
diff --git a/Eigen/src/Core/util/Memory.h b/Eigen/src/Core/util/Memory.h
index c9517acfc..957c36bcf 100644
--- a/Eigen/src/Core/util/Memory.h
+++ b/Eigen/src/Core/util/Memory.h
@@ -506,47 +506,56 @@ template<typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_align
 
 /****************************************************************************/
 
-/** \internal Returns the index of the first element of the array that is well aligned for vectorization.
+/** \internal Returns the index of the first element of the array that is well aligned with respect to the requested \a Alignment.
   *
+  * \tparam Alignment requested alignment in Bytes.
   * \param array the address of the start of the array
   * \param size the size of the array
   *
-  * \note If no element of the array is well aligned, the size of the array is returned. Typically,
-  * for example with SSE, "well aligned" means 16-byte-aligned. If vectorization is disabled or if the
+  * \note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,
+  * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If
   * packet size for the given scalar type is 1, then everything is considered well-aligned.
   *
-  * \note If the scalar type is vectorizable, we rely on the following assumptions: sizeof(Scalar) is a
-  * power of 2, the packet size in bytes is also a power of 2, and is a multiple of sizeof(Scalar). On the
-  * other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
+  * \note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a
+  * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
   * example with Scalar=double on certain 32-bit platforms, see bug #79.
   *
   * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
+  * \sa first_default_aligned()
   */
-template<typename Scalar, typename Index>
+template<int Alignment, typename Scalar, typename Index>
 inline Index first_aligned(const Scalar* array, Index size)
 {
-  static const Index PacketSize = packet_traits<Scalar>::size;
-  static const Index PacketAlignedMask = PacketSize-1;
+  static const Index ScalarSize = sizeof(Scalar);
+  static const Index AlignmentSize = Alignment / ScalarSize;
+  static const Index AlignmentMask = AlignmentSize-1;
 
-  if(PacketSize==1)
+  if(AlignmentSize<=1)
   {
-    // Either there is no vectorization, or a packet consists of exactly 1 scalar so that all elements
-    // of the array have the same alignment.
+    // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
+    // so that all elements of the array have the same alignment.
     return 0;
   }
-  else if(size_t(array) & (sizeof(Scalar)-1))
+  else if( (std::size_t(array) & (sizeof(Scalar)-1)) || (Alignment%ScalarSize)!=0)
   {
-    // There is vectorization for this scalar type, but the array is not aligned to the size of a single scalar.
+    // The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the scalar size.
     // Consequently, no element of the array is well aligned.
     return size;
   }
   else
   {
-    return std::min<Index>( (PacketSize - (Index((size_t(array)/sizeof(Scalar))) & PacketAlignedMask))
-                           & PacketAlignedMask, size);
+    return std::min<Index>( (AlignmentSize - (Index((std::size_t(array)/sizeof(Scalar))) & AlignmentMask)) & AlignmentMask, size);
   }
 }
 
+/** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.
+   * \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
+template<typename Scalar, typename Index>
+inline Index first_default_aligned(const Scalar* array, Index size)
+{
+  return first_aligned<packet_traits<Scalar>::size*sizeof(Scalar)>(array, size);
+}
+
 /** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
   */ 
 template<typename Index> 
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
index b7b83dcd2..55de15e87 100644
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -325,7 +325,7 @@ void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x
     // both vectors are sequentially stored in memory => vectorization
     enum { Peeling = 2 };
 
-    Index alignedStart = internal::first_aligned(y, size);
+    Index alignedStart = internal::first_default_aligned(y, size);
     Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
 
     const Packet pc = pset1<Packet>(c);
@@ -343,7 +343,7 @@ void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x
     Scalar* EIGEN_RESTRICT px = x + alignedStart;
     Scalar* EIGEN_RESTRICT py = y + alignedStart;
 
-    if(internal::first_aligned(x, size)==alignedStart)
+    if(internal::first_default_aligned(x, size)==alignedStart)
     {
       for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)
       {
diff --git a/Eigen/src/SparseLU/SparseLU_gemm_kernel.h b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
index 1d456ee0c..ae3685ac8 100644
--- a/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
+++ b/Eigen/src/SparseLU/SparseLU_gemm_kernel.h
@@ -39,9 +39,9 @@ void sparselu_gemm(Index m, Index n, Index d, const Scalar* A, Index lda, const
   };
   Index d_end = (d/RK)*RK;    // number of columns of A (rows of B) suitable for full register blocking
   Index n_end = (n/RN)*RN;    // number of columns of B-C suitable for processing RN columns at once
-  Index i0 = internal::first_aligned(A,m);
+  Index i0 = internal::first_default_aligned(A,m);
   
-  eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_aligned(C,m)));
+  eigen_internal_assert(((lda%PacketSize)==0) && ((ldc%PacketSize)==0) && (i0==internal::first_default_aligned(C,m)));
   
   // handle the non aligned rows of A and C without any optimization:
   for(Index i=0; i<i0; ++i)
diff --git a/Eigen/src/SparseLU/SparseLU_kernel_bmod.h b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
index 9513f8369..b8ea5f50f 100644
--- a/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
+++ b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h
@@ -66,8 +66,8 @@ EIGEN_DONT_INLINE void LU_kernel_bmod<SegSizeAtCompileTime>::run(const Index seg
   const Index PacketSize = internal::packet_traits<Scalar>::size;
   Index ldl = internal::first_multiple(nrow, PacketSize);
   Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(lda) );
-  Index aligned_offset = internal::first_aligned(tempv.data()+segsize, PacketSize);
-  Index aligned_with_B_offset = (PacketSize-internal::first_aligned(B.data(), PacketSize))%PacketSize;
+  Index aligned_offset = internal::first_default_aligned(tempv.data()+segsize, PacketSize);
+  Index aligned_with_B_offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize))%PacketSize;
   Map<Matrix<Scalar,Dynamic,1>, 0, OuterStride<> > l(tempv.data()+segsize+aligned_offset+aligned_with_B_offset, nrow, OuterStride<>(ldl) );
   
   l.setZero();
diff --git a/Eigen/src/SparseLU/SparseLU_panel_bmod.h b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
index bd3cf87b9..ca78406e0 100644
--- a/Eigen/src/SparseLU/SparseLU_panel_bmod.h
+++ b/Eigen/src/SparseLU/SparseLU_panel_bmod.h
@@ -145,7 +145,7 @@ void SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w,
       eigen_assert(tempv.size()>w*ldu + nrow*w + 1);
       
       Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
-      Index offset = (PacketSize-internal::first_aligned(B.data(), PacketSize)) % PacketSize;
+      Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
       Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
       
       L.setZero();
diff --git a/test/first_aligned.cpp b/test/first_aligned.cpp
index 467f94510..bf22f6b97 100644
--- a/test/first_aligned.cpp
+++ b/test/first_aligned.cpp
@@ -13,7 +13,7 @@ template<typename Scalar>
 void test_first_aligned_helper(Scalar *array, int size)
 {
   const int packet_size = sizeof(Scalar) * internal::packet_traits<Scalar>::size;
-  VERIFY(((size_t(array) + sizeof(Scalar) * internal::first_aligned(array, size)) % packet_size) == 0);
+  VERIFY(((size_t(array) + sizeof(Scalar) * internal::first_default_aligned(array, size)) % packet_size) == 0);
 }
 
 template<typename Scalar>
@@ -21,7 +21,7 @@ void test_none_aligned_helper(Scalar *array, int size)
 {
   EIGEN_UNUSED_VARIABLE(array);
   EIGEN_UNUSED_VARIABLE(size);
-  VERIFY(internal::packet_traits<Scalar>::size == 1 || internal::first_aligned(array, size) == size);
+  VERIFY(internal::packet_traits<Scalar>::size == 1 || internal::first_default_aligned(array, size) == size);
 }
 
 struct some_non_vectorizable_type { float x; };