diff --git a/math/mathcore/inc/Math/IFunction.h b/math/mathcore/inc/Math/IFunction.h
index afd88f14b193d..e7871c4f06f76 100644
--- a/math/mathcore/inc/Math/IFunction.h
+++ b/math/mathcore/inc/Math/IFunction.h
@@ -360,7 +360,7 @@ namespace ROOT {
             Gradient(x, df);
          }
 
-
+         virtual bool returnsInMinuit2ParameterSpace() const { return false; }
       };
 
 //___________________________________________________________________________________
diff --git a/math/minuit2/CMakeLists.txt b/math/minuit2/CMakeLists.txt
index fac5ca399789e..962ee4c78f71e 100644
--- a/math/minuit2/CMakeLists.txt
+++ b/math/minuit2/CMakeLists.txt
@@ -28,6 +28,7 @@ if(CMAKE_PROJECT_NAME STREQUAL ROOT)
       Minuit2/CombinedMinimumBuilder.h
       Minuit2/ContoursError.h
       Minuit2/DavidonErrorUpdator.h
+      Minuit2/ExternalInternalGradientCalculator.h
       Minuit2/FCNAdapter.h
       Minuit2/FCNBase.h
       Minuit2/FCNGradAdapter.h
@@ -128,6 +129,7 @@ if(CMAKE_PROJECT_NAME STREQUAL ROOT)
       src/CMakeLists.txt
       src/CombinedMinimumBuilder.cxx
       src/DavidonErrorUpdator.cxx
+      src/ExternalInternalGradientCalculator.cxx
       src/FitterUtil.h
       src/FumiliBuilder.cxx
       src/FumiliErrorUpdator.cxx
diff --git a/math/minuit2/inc/Minuit2/AnalyticalGradientCalculator.h b/math/minuit2/inc/Minuit2/AnalyticalGradientCalculator.h
index 1f9e0f0fcda8f..9037e91830ed2 100644
--- a/math/minuit2/inc/Minuit2/AnalyticalGradientCalculator.h
+++ b/math/minuit2/inc/Minuit2/AnalyticalGradientCalculator.h
@@ -35,7 +35,7 @@ class AnalyticalGradientCalculator : public GradientCalculator {
 
    virtual bool CheckGradient() const;
 
-private:
+protected:
    const FCNGradientBase &fGradCalc;
    const MnUserTransformation &fTransformation;
 };
diff --git a/math/minuit2/inc/Minuit2/ExternalInternalGradientCalculator.h b/math/minuit2/inc/Minuit2/ExternalInternalGradientCalculator.h
new file mode 100644
index 0000000000000..e3e8b8d6d1b15
--- /dev/null
+++ b/math/minuit2/inc/Minuit2/ExternalInternalGradientCalculator.h
@@ -0,0 +1,49 @@
+// @(#)root/minuit2:$Id$
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
+
+/**********************************************************************
+ *                                                                    *
+ * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
+ *                                                                    *
+ **********************************************************************/
+
+#ifndef ROOT_Minuit2_ExternalInternalGradientCalculator
+#define ROOT_Minuit2_ExternalInternalGradientCalculator
+
+#include "Minuit2/AnalyticalGradientCalculator.h"
+
+namespace ROOT {
+
+namespace Minuit2 {
+
+class FCNGradientBase;
+class MnUserTransformation;
+
+/// Similar to the AnalyticalGradientCalculator, the ExternalInternalGradientCalculator
+/// supplies Minuit with an externally calculated gradient. The main difference is that
+/// ExternalInternalGradientCalculator expects that the external gradient calculator does
+/// things in Minuit2-internal parameter space, which means many int2ext and ext2int
+/// transformation steps are not necessary. This avoids loss of precision in some cases,
+/// where trigonometrically transforming parameters back and forth can lose a few bits of
+/// floating point precision on every pass.
+
+class ExternalInternalGradientCalculator : public AnalyticalGradientCalculator {
+
+public:
+   ExternalInternalGradientCalculator(const FCNGradientBase &fcn, const MnUserTransformation &state)
+      : AnalyticalGradientCalculator(fcn, state)
+   {
+   }
+
+   ~ExternalInternalGradientCalculator() {}
+
+   virtual FunctionGradient operator()(const MinimumParameters &) const;
+
+   virtual FunctionGradient operator()(const MinimumParameters &, const FunctionGradient &) const;
+};
+
+} // namespace Minuit2
+
+} // namespace ROOT
+
+#endif // ROOT_Minuit2_ExternalInternalGradientCalculator
diff --git a/math/minuit2/inc/Minuit2/FCNGradAdapter.h b/math/minuit2/inc/Minuit2/FCNGradAdapter.h
index c33103902653c..6d42bab48f340 100644
--- a/math/minuit2/inc/Minuit2/FCNGradAdapter.h
+++ b/math/minuit2/inc/Minuit2/FCNGradAdapter.h
@@ -38,12 +38,12 @@ class FCNGradAdapter : public FCNGradientBase {
 
    ~FCNGradAdapter() {}
 
-   double operator()(const std::vector<double> &v) const { return fFunc.operator()(&v[0]); }
+   double operator()(const std::vector<double> &v) const override { return fFunc.operator()(&v[0]); }
    double operator()(const double *v) const { return fFunc.operator()(v); }
 
-   double Up() const { return fUp; }
+   double Up() const override { return fUp; }
 
-   std::vector<double> Gradient(const std::vector<double> &v) const
+   std::vector<double> Gradient(const std::vector<double> &v) const override
    {
       fFunc.Gradient(&v[0], &fGrad[0]);
 
@@ -56,7 +56,15 @@ class FCNGradAdapter : public FCNGradientBase {
    }
    // forward interface
    // virtual double operator()(int npar, double* params,int iflag = 4) const;
-   bool CheckGradient() const { return false; }
+   bool CheckGradient() const override { return false; }
+
+   GradientParameterSpace gradParameterSpace() const override {
+      if (fFunc.returnsInMinuit2ParameterSpace()) {
+         return GradientParameterSpace::Internal;
+      } else {
+         return GradientParameterSpace::External;
+      }
+   }
 
 private:
    const Function &fFunc;
diff --git a/math/minuit2/inc/Minuit2/FCNGradientBase.h b/math/minuit2/inc/Minuit2/FCNGradientBase.h
index 2fd6abebf83ac..4300528b65929 100644
--- a/math/minuit2/inc/Minuit2/FCNGradientBase.h
+++ b/math/minuit2/inc/Minuit2/FCNGradientBase.h
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -31,6 +31,10 @@ namespace Minuit2 {
     "false".
  */
 
+enum class GradientParameterSpace {
+  External, Internal
+};
+
 class FCNGradientBase : public FCNBase {
 
 public:
@@ -39,6 +43,11 @@ class FCNGradientBase : public FCNBase {
    virtual std::vector<double> Gradient(const std::vector<double> &) const = 0;
 
    virtual bool CheckGradient() const { return true; }
+
+   virtual GradientParameterSpace gradParameterSpace() const {
+      return GradientParameterSpace::External;
+   };
+
 };
 
 } // namespace Minuit2
diff --git a/math/minuit2/inc/Minuit2/SinParameterTransformation.h b/math/minuit2/inc/Minuit2/SinParameterTransformation.h
index 97c5c96620d9c..b21a20e2be750 100644
--- a/math/minuit2/inc/Minuit2/SinParameterTransformation.h
+++ b/math/minuit2/inc/Minuit2/SinParameterTransformation.h
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -28,9 +28,9 @@ class SinParameterTransformation {
 
    ~SinParameterTransformation() {}
 
-   double Int2ext(double Value, double Upper, double Lower) const;
-   double Ext2int(double Value, double Upper, double Lower, const MnMachinePrecision &) const;
-   double DInt2Ext(double Value, double Upper, double Lower) const;
+   long double Int2ext(long double Value, long double Upper, long double Lower) const;
+   long double Ext2int(long double Value, long double Upper, long double Lower, const MnMachinePrecision &) const;
+   long double DInt2Ext(long double Value, long double Upper, long double Lower) const;
 
 private:
 };
diff --git a/math/minuit2/inc/Minuit2/SqrtLowParameterTransformation.h b/math/minuit2/inc/Minuit2/SqrtLowParameterTransformation.h
index e38558520cdc3..a9185dc1b7fda 100644
--- a/math/minuit2/inc/Minuit2/SqrtLowParameterTransformation.h
+++ b/math/minuit2/inc/Minuit2/SqrtLowParameterTransformation.h
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -35,13 +35,13 @@ class SqrtLowParameterTransformation /* : public ParameterTransformation */ {
    ~SqrtLowParameterTransformation() {}
 
    // transformation from internal to external
-   double Int2ext(double Value, double Lower) const;
+   long double Int2ext(long double Value, long double Lower) const;
 
    // transformation from external to internal
-   double Ext2int(double Value, double Lower, const MnMachinePrecision &) const;
+   long double Ext2int(long double Value, long double Lower, const MnMachinePrecision &) const;
 
    // derivative of transformation from internal to external
-   double DInt2Ext(double Value, double Lower) const;
+   long double DInt2Ext(long double Value, long double Lower) const;
 
 private:
 };
diff --git a/math/minuit2/inc/Minuit2/SqrtUpParameterTransformation.h b/math/minuit2/inc/Minuit2/SqrtUpParameterTransformation.h
index 7e744306d98b0..8cbfa1a71b8ab 100644
--- a/math/minuit2/inc/Minuit2/SqrtUpParameterTransformation.h
+++ b/math/minuit2/inc/Minuit2/SqrtUpParameterTransformation.h
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -36,13 +36,13 @@ class SqrtUpParameterTransformation /* : public ParameterTransformation */ {
    ~SqrtUpParameterTransformation() {}
 
    // transformation from internal to external
-   double Int2ext(double Value, double Upper) const;
+   long double Int2ext(long double Value, long double Upper) const;
 
    // transformation from external to internal
-   double Ext2int(double Value, double Upper, const MnMachinePrecision &) const;
+   long double Ext2int(long double Value, long double Upper, const MnMachinePrecision &) const;
 
    // derivative of transformation from internal to external
-   double DInt2Ext(double Value, double Upper) const;
+   long double DInt2Ext(long double Value, long double Upper) const;
 
 private:
 };
diff --git a/math/minuit2/src/CMakeLists.txt b/math/minuit2/src/CMakeLists.txt
index 33020a0c421ca..957f53ceda4f2 100644
--- a/math/minuit2/src/CMakeLists.txt
+++ b/math/minuit2/src/CMakeLists.txt
@@ -17,6 +17,7 @@ set(MINUIT2_HEADERS
     CombinedMinimumBuilder.h
     ContoursError.h
     DavidonErrorUpdator.h
+    ExternalInternalGradientCalculator.h
     FCNAdapter.h
     FCNBase.h
     FCNGradAdapter.h
@@ -117,6 +118,7 @@ set(MINUIT2_SOURCES
     BFGSErrorUpdator.cxx
     CombinedMinimumBuilder.cxx
     DavidonErrorUpdator.cxx
+    ExternalInternalGradientCalculator.cxx
     FumiliBuilder.cxx
     FumiliErrorUpdator.cxx
     FumiliGradientCalculator.cxx
diff --git a/math/minuit2/src/ExternalInternalGradientCalculator.cxx b/math/minuit2/src/ExternalInternalGradientCalculator.cxx
new file mode 100644
index 0000000000000..19700394fc9d7
--- /dev/null
+++ b/math/minuit2/src/ExternalInternalGradientCalculator.cxx
@@ -0,0 +1,53 @@
+// @(#)root/minuit2:$Id$
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
+
+/**********************************************************************
+ *                                                                    *
+ * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
+ *                                                                    *
+ **********************************************************************/
+
+#include <vector>
+#include "Minuit2/ExternalInternalGradientCalculator.h"
+#include "Minuit2/FCNGradientBase.h"
+#include "Minuit2/MnUserTransformation.h"
+#include "Minuit2/FunctionGradient.h"
+#include "Minuit2/MinimumParameters.h"
+
+namespace ROOT {
+namespace Minuit2 {
+
+FunctionGradient ExternalInternalGradientCalculator::operator()(const MinimumParameters &par) const
+{
+   // evaluate analytical gradient. take care of parameter transformations
+   std::vector<double> par_vec;
+   par_vec.resize(par.Vec().size());
+   for (std::size_t ix = 0; ix < par.Vec().size(); ++ix) {
+      par_vec[ix] = par.Vec()(ix);
+   }
+
+   std::vector<double> grad = fGradCalc.Gradient(par_vec);
+   assert(grad.size() == fTransformation.Parameters().size());
+
+   MnAlgebraicVector v(par.Vec().size());
+   for (unsigned int i = 0; i < par.Vec().size(); i++) {
+      unsigned int ext = fTransformation.ExtOfInt(i);
+      v(i) = grad[ext];
+   }
+
+#ifdef DEBUG
+   std::cout << "User given gradient in Minuit2" << v << std::endl;
+#endif
+
+   return FunctionGradient(v);
+}
+
+FunctionGradient
+ExternalInternalGradientCalculator::operator()(const MinimumParameters &par, const FunctionGradient &) const
+{
+   // needed from base class
+   return (*this)(par);
+}
+
+} // namespace Minuit2
+} // namespace ROOT
diff --git a/math/minuit2/src/ModularFunctionMinimizer.cxx b/math/minuit2/src/ModularFunctionMinimizer.cxx
index b14d18c3b84da..82541dc86dba0 100644
--- a/math/minuit2/src/ModularFunctionMinimizer.cxx
+++ b/math/minuit2/src/ModularFunctionMinimizer.cxx
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -10,6 +10,7 @@
 #include "Minuit2/ModularFunctionMinimizer.h"
 #include "Minuit2/MinimumSeedGenerator.h"
 #include "Minuit2/AnalyticalGradientCalculator.h"
+#include "Minuit2/ExternalInternalGradientCalculator.h"
 #include "Minuit2/Numerical2PGradientCalculator.h"
 #include "Minuit2/MinimumBuilder.h"
 #include "Minuit2/MinimumSeed.h"
@@ -148,7 +149,14 @@ FunctionMinimum ModularFunctionMinimizer::Minimize(const FCNGradientBase &fcn, c
    // Create the minuit FCN wrapper (MnUserFcn) containing the trasformation (int<->ext)
 
    MnUserFcn mfcn(fcn, st.Trafo());
-   AnalyticalGradientCalculator gc(fcn, st.Trafo());
+   AnalyticalGradientCalculator *gc;
+   if (fcn.gradParameterSpace() == GradientParameterSpace::Internal) {
+        //        std::cout << "-- ModularFunctionMinimizer::Minimize: Internal parameter space" << std::endl;
+        gc = new ExternalInternalGradientCalculator(fcn, st.Trafo());
+   } else {
+        //        std::cout << "-- ModularFunctionMinimizer::Minimize: External parameter space" << std::endl;
+        gc = new AnalyticalGradientCalculator(fcn, st.Trafo());
+   }
 
    unsigned int npar = st.VariableParameters();
    if (maxfcn == 0)
@@ -158,7 +166,11 @@ FunctionMinimum ModularFunctionMinimizer::Minimize(const FCNGradientBase &fcn, c
    Numerical2PGradientCalculator numgc(mfcn, st.Trafo(), strategy);
    MinimumSeed mnseeds = SeedGenerator()(mfcn, numgc, st, strategy);
 
-   return Minimize(mfcn, gc, mnseeds, strategy, maxfcn, toler);
+   auto minimum = Minimize(mfcn, *gc, mnseeds, strategy, maxfcn, toler);
+
+   delete gc;
+
+   return minimum;
 }
 
 FunctionMinimum ModularFunctionMinimizer::Minimize(const MnFcn &mfcn, const GradientCalculator &gc,
diff --git a/math/minuit2/src/SinParameterTransformation.cxx b/math/minuit2/src/SinParameterTransformation.cxx
index 03355a4ccb8b8..7e491725118a8 100644
--- a/math/minuit2/src/SinParameterTransformation.cxx
+++ b/math/minuit2/src/SinParameterTransformation.cxx
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -16,25 +16,25 @@ namespace ROOT {
 
 namespace Minuit2 {
 
-double SinParameterTransformation::Int2ext(double Value, double Upper, double Lower) const
+long double SinParameterTransformation::Int2ext(long double Value, long double Upper, long double Lower) const
 {
    // transformation from  to internal (unlimited) to external values (limited by Lower/Upper )
    return Lower + 0.5 * (Upper - Lower) * (std::sin(Value) + 1.);
 }
 
-double
-SinParameterTransformation::Ext2int(double Value, double Upper, double Lower, const MnMachinePrecision &prec) const
+long double
+SinParameterTransformation::Ext2int(long double Value, long double Upper, long double Lower, const MnMachinePrecision &prec) const
 {
    // transformation from external (limited by Lower/Upper )  to internal (unlimited) values given the lower/upper
    // limits
 
-   double piby2 = 2. * std::atan(1.);
-   double distnn = 8. * std::sqrt(prec.Eps2());
-   double vlimhi = piby2 - distnn;
-   double vlimlo = -piby2 + distnn;
+   long double piby2 = 2. * std::atan(1.);
+   long double distnn = 8. * std::sqrt(prec.Eps2());
+   long double vlimhi = piby2 - distnn;
+   long double vlimlo = -piby2 + distnn;
 
-   double yy = 2. * (Value - Lower) / (Upper - Lower) - 1.;
-   double yy2 = yy * yy;
+   long double yy = 2. * (Value - Lower) / (Upper - Lower) - 1.;
+   long double yy2 = yy * yy;
    if (yy2 > (1. - prec.Eps2())) {
       if (yy < 0.) {
          // Lower limit
@@ -45,13 +45,12 @@ SinParameterTransformation::Ext2int(double Value, double Upper, double Lower, co
          //       std::cout<<"SinParameterTransformation warning: is at its Upper allowed limit."<<std::endl;
          return vlimhi;
       }
-
    } else {
       return std::asin(yy);
    }
 }
 
-double SinParameterTransformation::DInt2Ext(double Value, double Upper, double Lower) const
+long double SinParameterTransformation::DInt2Ext(long double Value, long double Upper, long double Lower) const
 {
    // return the derivative of the transformation d Ext/ d Int
    return 0.5 * ((Upper - Lower) * std::cos(Value));
diff --git a/math/minuit2/src/SqrtLowParameterTransformation.cxx b/math/minuit2/src/SqrtLowParameterTransformation.cxx
index df813899fa41c..ab362e9b3cf0c 100644
--- a/math/minuit2/src/SqrtLowParameterTransformation.cxx
+++ b/math/minuit2/src/SqrtLowParameterTransformation.cxx
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -19,28 +19,29 @@ namespace ROOT {
 
 namespace Minuit2 {
 
-double SqrtLowParameterTransformation::Int2ext(double value, double lower) const
+long double SqrtLowParameterTransformation::Int2ext(long double value, long double lower) const
 {
    /// internal to external transformation
-   double val = lower - 1. + std::sqrt(value * value + 1.);
+   long double val = lower - 1. + std::sqrt(value * value + 1.);
    return val;
 }
 
-double SqrtLowParameterTransformation::Ext2int(double value, double lower, const MnMachinePrecision &) const
+long double
+SqrtLowParameterTransformation::Ext2int(long double value, long double lower, const MnMachinePrecision &) const
 {
    // external to internal transformation
-   double yy = value - lower + 1.;
-   double yy2 = yy * yy;
+   long double yy = value - lower + 1.;
+   long double yy2 = yy * yy;
    if (yy2 < 1.)
       return 0;
    else
       return std::sqrt(yy2 - 1);
 }
 
-double SqrtLowParameterTransformation::DInt2Ext(double value, double) const
+long double SqrtLowParameterTransformation::DInt2Ext(long double value, long double) const
 {
    // derivative of internal to external transofrmation   :  d (Int2Ext) / d Int
-   double val = value / (std::sqrt(value * value + 1.));
+   long double val = value / (std::sqrt(value * value + 1.));
    return val;
 }
 
diff --git a/math/minuit2/src/SqrtUpParameterTransformation.cxx b/math/minuit2/src/SqrtUpParameterTransformation.cxx
index cb9e70ccd2689..439ac748969d2 100644
--- a/math/minuit2/src/SqrtUpParameterTransformation.cxx
+++ b/math/minuit2/src/SqrtUpParameterTransformation.cxx
@@ -1,5 +1,5 @@
 // @(#)root/minuit2:$Id$
-// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005
+// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
 /**********************************************************************
  *                                                                    *
@@ -19,28 +19,28 @@ namespace ROOT {
 
 namespace Minuit2 {
 
-double SqrtUpParameterTransformation::Int2ext(double value, double upper) const
+long double SqrtUpParameterTransformation::Int2ext(long double value, long double upper) const
 {
    // internal to external transformation
-   double val = upper + 1. - std::sqrt(value * value + 1.);
+   long double val = upper + 1. - std::sqrt(value * value + 1.);
    return val;
 }
 
-double SqrtUpParameterTransformation::Ext2int(double value, double upper, const MnMachinePrecision &) const
+long double SqrtUpParameterTransformation::Ext2int(long double value, long double upper, const MnMachinePrecision &) const
 {
    // external to internal transformation
-   double yy = upper - value + 1.;
-   double yy2 = yy * yy;
+   long double yy = upper - value + 1.;
+   long double yy2 = yy * yy;
    if (yy2 < 1.)
       return 0;
    else
       return std::sqrt(yy2 - 1);
 }
 
-double SqrtUpParameterTransformation::DInt2Ext(double value, double) const
+long double SqrtUpParameterTransformation::DInt2Ext(long double value, long double) const
 {
    // derivative of internal to external transofrmation :  d (Int2Ext ) / d Int
-   double val = -value / (std::sqrt(value * value + 1.));
+   long double val = -value / (std::sqrt(value * value + 1.));
    return val;
 }