diff --git a/include/ceres/internal/port.h b/include/ceres/internal/port.h
index e57049d..1193fcf 100644
--- a/include/ceres/internal/port.h
+++ b/include/ceres/internal/port.h
@@ -35,7 +35,7 @@
 #ifdef __cplusplus
 
 #include "ceres/internal/config.h"
-
+#include "Eigen/Core"
 #if defined(CERES_TR1_MEMORY_HEADER)
 #include <tr1/memory>
 #else
@@ -50,6 +50,41 @@
 using std::shared_ptr;
 #endif
 
+// We allocate some Eigen objects on the stack and other places they
+// might not be aligned to 16-byte boundaries.  If we have C++11, we
+// can specify their alignment anyway, and thus can safely enable
+// vectorization on those matrices; in C++99, we are out of luck.  Figure out
+// what case we're in and write macros that do the right thing.
+#ifdef CERES_USE_CXX11
+namespace port_constants {
+
+static constexpr size_t kMaxAlignBytes =
+    // Work around a GCC 4.8 bug
+    // (https://gcc.gnu.org/bugzilla/show_bug.cgi?id=56019) where
+    // std::max_align_t is misplaced.
+#if defined (__GNUC__) && __GNUC__ == 4 && __GNUC_MINOR__ == 8
+    alignof(::max_align_t);
+#else
+    alignof(std::max_align_t);
+#endif
+
+static constexpr bool kShouldAlignMatrix = 16 <= kMaxAlignBytes;
+static constexpr size_t kAlignment = kShouldAlignMatrix ? 16 : 1;
+
+static constexpr int kEigenAlignmentHint =
+    kShouldAlignMatrix ? Eigen::AutoAlign : Eigen::DontAlign;
+}  // namespace port_constants
+
+#define CERES_ALIGNMENT_SPECIFIER alignas(::ceres::port_constants::kAlignment)
+#define CERES_MATRIX_ALIGN_HINT ::ceres::port_constants::kEigenAlignmentHint
+
+#else // !CXX_11
+
+#define CERES_ALIGNMENT_SPECIFIER
+#define CERES_MATRIX_ALIGN_HINT Eigen::DontAlign
+
+#endif
+
 }  // namespace ceres
 
 #endif  // __cplusplus
diff --git a/include/ceres/jet.h b/include/ceres/jet.h
index a21fd7a..8515be8 100644
--- a/include/ceres/jet.h
+++ b/include/ceres/jet.h
@@ -164,6 +164,7 @@
 
 #include "Eigen/Core"
 #include "ceres/fpclassify.h"
+#include "ceres/internal/port.h"
 
 namespace ceres {
 
@@ -227,21 +228,8 @@
   T a;
 
   // The infinitesimal part.
-  //
-  // Note the Eigen::DontAlign bit is needed here because this object
-  // gets allocated on the stack and as part of other arrays and
-  // structs. Forcing the right alignment there is the source of much
-  // pain and suffering. Even if that works, passing Jets around to
-  // functions by value has problems because the C++ ABI does not
-  // guarantee alignment for function arguments.
-  //
-  // Setting the DontAlign bit prevents Eigen from using SSE for the
-  // various operations on Jets. This is a small performance penalty
-  // since the AutoDiff code will still expose much of the code as
-  // statically sized loops to the compiler. But given the subtle
-  // issues that arise due to alignment, especially when dealing with
-  // multiple platforms, it seems to be a trade off worth making.
-  Eigen::Matrix<T, N, 1, Eigen::DontAlign> v;
+  // See ceres/include/internal/port.h for meaning of the #defines here.
+  CERES_ALIGNMENT_SPECIFIER Eigen::Matrix<T, N, 1, CERES_MATRIX_ALIGN_HINT> v;
 };
 
 // Unary +