diff --git a/math/minuit2/inc/Minuit2/MnStrategy.h b/math/minuit2/inc/Minuit2/MnStrategy.h
index 519bf832dfaef..dafa4d108e619 100644
--- a/math/minuit2/inc/Minuit2/MnStrategy.h
+++ b/math/minuit2/inc/Minuit2/MnStrategy.h
@@ -131,6 +131,14 @@ namespace Minuit2 {
       the case of high stats) and the forward finite difference (default)
       behaviour leads incorrectly to a non-positive-definite covariance
       matrix.
+
+      The strategy level only sets the defaults: when Minuit2 is used through
+      ROOT::Minuit2::Minuit2Minimizer, the tunables listed below can also be overridden
+      individually, by name, through the "Minuit2" extra options of
+      ROOT::Math::MinimizerOptions. That is the way to pick up a single behaviour of a
+      higher strategy (most usefully **HessianCentralFDMixedDerivatives**) without
+      paying for all the others.
+
        </td>
      </tr>
      <tr>
diff --git a/math/minuit2/src/Minuit2Minimizer.cxx b/math/minuit2/src/Minuit2Minimizer.cxx
index 748869c8f53d8..9788394f02d09 100644
--- a/math/minuit2/src/Minuit2Minimizer.cxx
+++ b/math/minuit2/src/Minuit2Minimizer.cxx
@@ -443,6 +443,11 @@ ROOT::Minuit2::MnStrategy customizedStrategy(unsigned int strategyLevel, ROOT::M
    st.SetHessianStepTolerance(customize("HessianStepTolerance", st.HessianStepTolerance()));
    st.SetHessianG2Tolerance(customize("HessianG2Tolerance", st.HessianG2Tolerance()));
 
+   // These two are the parts of strategy 3 that matter most for ill-conditioned problems
+   st.SetHessianCentralFDMixedDerivatives(
+      customize("HessianCentralFDMixedDerivatives", int(st.HessianCentralFDMixedDerivatives())));
+   st.SetHessianForcePosDef(customize("HessianForcePosDef", int(st.HessianForcePosDef())));
+
    return st;
 }