diff --git a/include/schaapcommon/h5parm/jonesparameters.h b/include/schaapcommon/h5parm/jonesparameters.h
index 54345038a6810d3b621f414a4b0a1ecdf1812acc..b354915e40b343bf6f701df8fdea33bdaae1b7c6 100644
--- a/include/schaapcommon/h5parm/jonesparameters.h
+++ b/include/schaapcommon/h5parm/jonesparameters.h
@@ -70,8 +70,6 @@ class JonesParameters {
    * (e.g. phase and amplitude). These are the parameters as they are
    * stored (e.g. TEC values).
    * \param invert (optional default=false) Invert the parameters
-   * \param sigma_mmse (optional default=0.) Minimum mean square error parameter
-   * (remnant from BBS times, leave at 0 unless you know what you're doing).
    */
   JonesParameters(const std::vector<double>& freqs,
                   const std::vector<double>& times,
@@ -79,7 +77,7 @@ class JonesParameters {
                   GainType gain_type, InterpolationType interpolation_type,
                   hsize_t direction,
                   std::vector<std::vector<std::vector<double>>>&& parm_values,
-                  bool invert = false, float sigma_mmse = 0.);
+                  bool invert = false);
 
   /**
    * Constructor for JonesParameters with given parm_values. To be used if
@@ -91,14 +89,12 @@ class JonesParameters {
    * \param correct_type Correction type of the Jones matrix
    * \param solution Solution in format [n_ants * n_pols, n_chans]
    * \param invert (optional default=false) Invert the parameters
-   * \param sigma_mmse (optional default=0.) Minimum mean square error parameter
-   * (remnant from BBS times, leave at 0 unless you know what you're doing).
    */
   JonesParameters(
       const std::vector<double>& freqs, const std::vector<double>& times,
       const std::vector<std::string>& antenna_names, GainType gain_type,
       const std::vector<std::vector<std::complex<double>>>& solution,
-      bool invert = false, float sigma_mmse = 0.);
+      bool invert = false);
 
   /**
    * Contructor for JonesParameters. JonesParameters will extract parameter
@@ -113,8 +109,6 @@ class JonesParameters {
    * \param sol_tab2 (optional default=nullptr) soltab with parameters for
    * complex values. Shapes of sol_tab and sol_tab2 can differ
    * \param invert (optional default=false) Invert the parameters
-   * \param sigma_mmse (optional default=0.) Minimum mean square error parameter
-   * (remnant from BBS times, leave at 0 unless you know what you're doing)
    * \param parm_size (optional default=0) allows to override the vector size
    * for parm_values
    * \param missing_antenna_behavior (optional default=kError) what to do with
@@ -126,8 +120,7 @@ class JonesParameters {
                   GainType gain_type, InterpolationType interpolation_type,
                   hsize_t direction, schaapcommon::h5parm::SolTab* sol_tab,
                   schaapcommon::h5parm::SolTab* sol_tab2 = nullptr,
-                  bool invert = false, float sigma_mmse = 0.,
-                  size_t parm_size = 0,
+                  bool invert = false, size_t parm_size = 0,
                   MissingAntennaBehavior missing_antenna_behavior =
                       MissingAntennaBehavior::kError);
 
@@ -214,12 +207,10 @@ class JonesParameters {
    * in MakeComplex.
    * \param parms Reference to the complex parameters that will be inverted
    * obtained via MakeComplex
-   * \param sigma_mmse (optional default=0.) Minimum mean square error parameter
-   * (remnant from BBS times, leave at 0 unless you know what you're doing).
    * \param correct_type Correction type of the Jones matrix
    */
   static void Invert(casacore::Cube<std::complex<float>>& parms,
-                     float sigma_mmse, GainType gain_type);
+                     GainType gain_type);
 
   /// Stored Jones matrices, dimensions (nparms, nantenna, ntime*nfreq),
   /// frequency varies fastest. nparms is 2 for diagonal, 4 for full jones
diff --git a/src/h5parm/jonesparameters.cc b/src/h5parm/jonesparameters.cc
index 119c4c8a5077bd21f961771c97069eb31b202fff..eecd0ebe48a5b87d510e0a3d361dfc73eddd22d5 100644
--- a/src/h5parm/jonesparameters.cc
+++ b/src/h5parm/jonesparameters.cc
@@ -27,23 +27,22 @@ JonesParameters::JonesParameters(
     const std::vector<double>& freqs, const std::vector<double>& times,
     const std::vector<std::string>& antenna_names, GainType gain_type,
     InterpolationType interpolation_type, hsize_t direction,
-    std::vector<std::vector<std::vector<double>>>&& parm_values, bool invert,
-    float sigma_mmse) {
+    std::vector<std::vector<std::vector<double>>>&& parm_values, bool invert) {
   const size_t num_parms = GetNParms(gain_type);
   parms_.resize(num_parms, antenna_names.size(), freqs.size() * times.size());
   for (size_t ant = 0; ant < antenna_names.size(); ++ant) {
     MakeComplex(parm_values, ant, freqs, gain_type, invert);
   }
   if (invert) {
-    Invert(parms_, sigma_mmse, gain_type);
+    Invert(parms_, gain_type);
   }
 }
 
 JonesParameters::JonesParameters(
     const std::vector<double>& freqs, const std::vector<double>& times,
     const std::vector<std::string>& antenna_names, GainType gain_type,
-    const std::vector<std::vector<std::complex<double>>>& solution, bool invert,
-    float sigma_mmse) {
+    const std::vector<std::vector<std::complex<double>>>& solution,
+    bool invert) {
   /*
    * Solution is in format [n_ants * n_pols, n_chans]
    * Expected format of the parm_values is [n_chans, n_ants, n_pols]
@@ -62,7 +61,7 @@ JonesParameters::JonesParameters(
   }
 
   if (invert) {
-    Invert(parms_, sigma_mmse, gain_type);
+    Invert(parms_, gain_type);
   }
 }
 
@@ -71,8 +70,8 @@ JonesParameters::JonesParameters(
     const std::vector<std::string>& antenna_names, GainType gain_type,
     InterpolationType interpolation_type, hsize_t direction,
     schaapcommon::h5parm::SolTab* sol_tab,
-    schaapcommon::h5parm::SolTab* sol_tab2, bool invert, float sigma_mmse,
-    size_t parm_size, MissingAntennaBehavior missing_antenna_behavior) {
+    schaapcommon::h5parm::SolTab* sol_tab2, bool invert, size_t parm_size,
+    MissingAntennaBehavior missing_antenna_behavior) {
   const size_t num_parms = GetNParms(gain_type);
 
   parms_.resize(num_parms, antenna_names.size(), freqs.size() * times.size());
@@ -124,7 +123,7 @@ JonesParameters::JonesParameters(
     }
   }
   if (invert) {
-    Invert(parms_, sigma_mmse, gain_type);
+    Invert(parms_, gain_type);
   }
 }
 
@@ -315,7 +314,7 @@ void JonesParameters::FillParmValues(
 }
 
 void JonesParameters::Invert(casacore::Cube<casacore::Complex>& parms,
-                             float sigma_mmse, GainType gain_type) {
+                             GainType gain_type) {
   const size_t tf_size = parms.shape()[2];
   const size_t ant_size = parms.shape()[1];
   for (size_t tf = 0; tf < tf_size; ++tf) {
@@ -326,12 +325,6 @@ void JonesParameters::Invert(casacore::Cube<casacore::Complex>& parms,
       } else if (gain_type == GainType::kFullJones ||
                  gain_type == GainType::kFullJonesRealImaginary) {
         aocommon::MC2x2F v(&parms(0, ant, tf));
-
-        // Add the variance of the nuisance term to the elements on the
-        // diagonal.
-        const float variance = sigma_mmse * sigma_mmse;
-        v[0] += variance;
-        v[3] += variance;
         v.Invert();
         v.AssignTo(&parms(0, ant, tf));
       } else if (gain_type == GainType::kRotationMeasure ||
diff --git a/src/h5parm/test/tjonesparameters.cc b/src/h5parm/test/tjonesparameters.cc
index 19decd9f41f8716cd2f9dd281a6b7144ef648e3e..496f73251301eaa9bcaec83a8b2185f93c89bc6b 100644
--- a/src/h5parm/test/tjonesparameters.cc
+++ b/src/h5parm/test/tjonesparameters.cc
@@ -46,7 +46,6 @@ class SolTabMock : public SolTab {
 };
 
 JonesParameters PrepareJonesParameters(GainType ct, bool invert = false,
-                                       float sigma_mmse = 0.,
                                        size_t parm_size = 0) {
   std::vector<std::string> antNames;
   for (size_t i = 0; i < kNAnts; ++i) {
@@ -59,8 +58,7 @@ JonesParameters PrepareJonesParameters(GainType ct, bool invert = false,
   SolTabMock mock2 = SolTabMock();
 
   JonesParameters jones(kFreqs, kTimes, antNames, ct, kInterpolationType,
-                        kDirection, &mock, &mock2, invert, sigma_mmse,
-                        parm_size);
+                        kDirection, &mock, &mock2, invert, parm_size);
   return jones;
 }
 
@@ -91,17 +89,16 @@ BOOST_AUTO_TEST_CASE(make_scalar_gain) {
 }
 
 BOOST_AUTO_TEST_CASE(make_complex_fulljones) {
-  JonesParameters jones =
-      PrepareJonesParameters(GainType::kFullJones, true, 1.);
+  JonesParameters jones = PrepareJonesParameters(GainType::kFullJones, true);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_EQUAL(parms.shape()[0], 4);
-  BOOST_CHECK_CLOSE(parms(0, 0, 0).real(), 0.5006091, 1e-3);
-  BOOST_CHECK_CLOSE(parms(0, 0, 0).imag(), 0.00108991, 1e-3);
+  BOOST_CHECK_CLOSE(parms(0, 0, 0).real(), 97.437, 1e-3);
+  BOOST_CHECK_CLOSE(parms(0, 0, 0).imag(), -174.659, 1e-3);
 }
 
 BOOST_AUTO_TEST_CASE(make_complex_tec) {
-  JonesParameters jones = PrepareJonesParameters(GainType::kTec, false, 0., 1U);
+  JonesParameters jones = PrepareJonesParameters(GainType::kTec, false, 1U);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_EQUAL(parms.shape()[0], 2);
@@ -110,7 +107,7 @@ BOOST_AUTO_TEST_CASE(make_complex_tec) {
 }
 
 BOOST_AUTO_TEST_CASE(make_complex_tec2) {
-  JonesParameters jones = PrepareJonesParameters(GainType::kTec, true, 0., 2U);
+  JonesParameters jones = PrepareJonesParameters(GainType::kTec, true, 2U);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_CLOSE(parms(0, 0, 0).real(), -0.993747, 1e-3);
@@ -146,7 +143,7 @@ BOOST_AUTO_TEST_CASE(make_complex_r_measure) {
 
 BOOST_AUTO_TEST_CASE(make_complex_r_measure_inverted) {
   JonesParameters jones =
-      PrepareJonesParameters(GainType::kRotationMeasure, true, 0.5, 4);
+      PrepareJonesParameters(GainType::kRotationMeasure, true, 4);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_CLOSE(parms(0, 0, 0).real(), -0.185403, 1e-3);
@@ -190,8 +187,7 @@ BOOST_AUTO_TEST_CASE(make_scalar_amplitude) {
 }
 
 BOOST_AUTO_TEST_CASE(make_complex_clock) {
-  JonesParameters jones =
-      PrepareJonesParameters(GainType::kClock, false, 0., 1U);
+  JonesParameters jones = PrepareJonesParameters(GainType::kClock, false, 1U);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_EQUAL(parms.shape()[0], 2);
@@ -200,8 +196,7 @@ BOOST_AUTO_TEST_CASE(make_complex_clock) {
 }
 
 BOOST_AUTO_TEST_CASE(make_complex_clock2) {
-  JonesParameters jones =
-      PrepareJonesParameters(GainType::kClock, true, 50, 2U);
+  JonesParameters jones = PrepareJonesParameters(GainType::kClock, true, 2U);
   const auto parms = jones.GetParms();
 
   BOOST_CHECK_CLOSE(parms(0, 0, 0).real(), 1., 1e-3);
@@ -272,7 +267,7 @@ BOOST_AUTO_TEST_CASE(missing_antenna_flag) {
 
   JonesParameters jones(kFreqs, kTimes, antNames, GainType::kDiagonalAmplitude,
                         kInterpolationType, kDirection, &mock, nullptr, false,
-                        0, 0, JonesParameters::MissingAntennaBehavior::kFlag);
+                        0, JonesParameters::MissingAntennaBehavior::kFlag);
 
   const auto parms = jones.GetParms();
   BOOST_CHECK_EQUAL(parms.shape()[1], kNAnts + 1);
@@ -292,7 +287,7 @@ BOOST_AUTO_TEST_CASE(missing_antenna_unit_diag) {
 
   JonesParameters jones(kFreqs, kTimes, antNames, GainType::kDiagonalAmplitude,
                         kInterpolationType, kDirection, &mock, nullptr, false,
-                        0, 0, JonesParameters::MissingAntennaBehavior::kUnit);
+                        0, JonesParameters::MissingAntennaBehavior::kUnit);
 
   const auto parms = jones.GetParms();
   BOOST_CHECK_EQUAL(parms.shape()[0], 2);
@@ -314,7 +309,7 @@ BOOST_AUTO_TEST_CASE(missing_antenna_unit_full) {
 
   JonesParameters jones(kFreqs, kTimes, antNames, GainType::kRotationAngle,
                         kInterpolationType, kDirection, &mock, nullptr, false,
-                        0, 0, JonesParameters::MissingAntennaBehavior::kUnit);
+                        0, JonesParameters::MissingAntennaBehavior::kUnit);
 
   const auto parms = jones.GetParms();
   BOOST_CHECK_EQUAL(parms.shape()[0], 4);