diff --git a/include/ceres/internal/autodiff.h b/include/ceres/internal/autodiff.h
index 72b8e37..0bc41f2 100644
--- a/include/ceres/internal/autodiff.h
+++ b/include/ceres/internal/autodiff.h
@@ -144,6 +144,7 @@
 
 #include <array>
 
+#include "ceres/internal/array_selector.h"
 #include "ceres/internal/eigen.h"
 #include "ceres/internal/fixed_array.h"
 #include "ceres/internal/parameter_dims.h"
@@ -152,6 +153,17 @@
 #include "ceres/types.h"
 #include "glog/logging.h"
 
+// If the number of parameters exceeds this values, the corresponding jets are
+// placed on the heap. This will reduce performance by a factor of 2-5 on
+// current compilers.
+#ifndef CERES_AUTODIFF_MAX_PARAMETERS_ON_STACK
+#define CERES_AUTODIFF_MAX_PARAMETERS_ON_STACK 50
+#endif
+
+#ifndef CERES_AUTODIFF_MAX_RESIDUALS_ON_STACK
+#define CERES_AUTODIFF_MAX_RESIDUALS_ON_STACK 20
+#endif
+
 namespace ceres {
 namespace internal {
 
@@ -174,9 +186,7 @@
   DCHECK(src);
   DCHECK(dst);
   for (int j = 0; j < N; ++j) {
-    dst[j].a = src[j];
-    dst[j].v.setZero();
-    dst[j].v[Offset + j] = T(1.0);
+    dst[j] = JetT(src[j], Offset + j);
   }
 }
 
@@ -284,38 +294,54 @@
           typename T>
 inline bool AutoDifferentiate(const Functor& functor,
                               T const* const* parameters,
-                              int num_outputs,
+                              int dynamic_num_outputs,
                               T* function_value,
                               T** jacobians) {
-  DCHECK_GT(num_outputs, 0);
-
   typedef Jet<T, ParameterDims::kNumParameters> JetT;
-  FixedArray<JetT, (256 * 7) / sizeof(JetT)> x(ParameterDims::kNumParameters +
-                                               num_outputs);
-
   using Parameters = typename ParameterDims::Parameters;
 
-  // These are the positions of the respective jets in the fixed array x.
+  if (kNumResiduals != DYNAMIC) {
+    DCHECK_EQ(kNumResiduals, dynamic_num_outputs);
+  }
+
+  ArraySelector<JetT,
+                ParameterDims::kNumParameters,
+                CERES_AUTODIFF_MAX_PARAMETERS_ON_STACK>
+      parameters_as_jets(ParameterDims::kNumParameters);
+
+  // Pointers to the beginning of each parameter block
   std::array<JetT*, ParameterDims::kNumParameterBlocks> unpacked_parameters =
-      ParameterDims::GetUnpackedParameters(x.data());
-  JetT* output = x.data() + ParameterDims::kNumParameters;
+      ParameterDims::GetUnpackedParameters(parameters_as_jets.data());
+
+  // If the number of residuals is fixed, we use the template argument as the
+  // number of outputs. Otherwise we use the num_outputs parameter. Note: The
+  // ?-operator here is compile-time evaluated, therefore num_outputs is also
+  // a compile-time constant for functors with fixed residuals.
+  const int num_outputs =
+      kNumResiduals == DYNAMIC ? dynamic_num_outputs : kNumResiduals;
+  DCHECK_GT(num_outputs, 0);
+
+  ArraySelector<JetT, kNumResiduals, CERES_AUTODIFF_MAX_RESIDUALS_ON_STACK>
+      residuals_as_jets(num_outputs);
 
   // Invalidate the output Jets, so that we can detect if the user
   // did not assign values to all of them.
   for (int i = 0; i < num_outputs; ++i) {
-    output[i].a = kImpossibleValue;
-    output[i].v.setConstant(kImpossibleValue);
+    residuals_as_jets[i].a = kImpossibleValue;
+    residuals_as_jets[i].v.setConstant(kImpossibleValue);
   }
 
-  Make1stOrderPerturbations<Parameters>::Apply(parameters, x.data());
+  Make1stOrderPerturbations<Parameters>::Apply(parameters,
+                                               parameters_as_jets.data());
 
   if (!VariadicEvaluate<ParameterDims>(
-          functor, unpacked_parameters.data(), output)) {
+          functor, unpacked_parameters.data(), residuals_as_jets.data())) {
     return false;
   }
 
-  Take0thOrderPart(num_outputs, output, function_value);
-  Take1stOrderParts<Parameters>::Apply(num_outputs, output, jacobians);
+  Take0thOrderPart(num_outputs, residuals_as_jets.data(), function_value);
+  Take1stOrderParts<Parameters>::Apply(
+      num_outputs, residuals_as_jets.data(), jacobians);
 
   return true;
 }
diff --git a/internal/ceres/autodiff_benchmarks/autodiff_benchmarks.cc b/internal/ceres/autodiff_benchmarks/autodiff_benchmarks.cc
index 89f56df..252cb52 100644
--- a/internal/ceres/autodiff_benchmarks/autodiff_benchmarks.cc
+++ b/internal/ceres/autodiff_benchmarks/autodiff_benchmarks.cc
@@ -78,7 +78,6 @@
   }
 }
 BENCHMARK(BM_Linear1AutoDiff)->Arg(0)->Arg(1);
-;
 
 #ifdef WITH_CODE_GENERATION
 static void BM_Linear10CodeGen(benchmark::State& state) {
@@ -98,7 +97,6 @@
   }
 }
 BENCHMARK(BM_Linear10CodeGen)->Arg(0)->Arg(1);
-;
 #endif
 
 static void BM_Linear10AutoDiff(benchmark::State& state) {
@@ -121,7 +119,6 @@
   }
 }
 BENCHMARK(BM_Linear10AutoDiff)->Arg(0)->Arg(1);
-;
 
 // From the NIST problem collection.
 struct Rat43CostFunctor {
@@ -185,7 +182,6 @@
   }
 }
 BENCHMARK(BM_SnavelyReprojectionCodeGen)->Arg(0)->Arg(1);
-;
 #endif
 
 static void BM_SnavelyReprojectionAutoDiff(benchmark::State& state) {
@@ -214,7 +210,6 @@
 }
 
 BENCHMARK(BM_SnavelyReprojectionAutoDiff)->Arg(0)->Arg(1);
-;
 
 #ifdef WITH_CODE_GENERATION
 static void BM_BrdfCodeGen(benchmark::State& state) {
@@ -252,7 +247,6 @@
 }
 
 BENCHMARK(BM_BrdfCodeGen)->Arg(0)->Arg(1);
-;
 #endif
 
 static void BM_BrdfAutoDiff(benchmark::State& state) {
@@ -292,7 +286,6 @@
 }
 
 BENCHMARK(BM_BrdfAutoDiff)->Arg(0)->Arg(1);
-;
 
 }  // namespace ceres