diff --git a/vmec/ideal_mhd_model/ideal_mhd_model_test.cc b/vmec/ideal_mhd_model/ideal_mhd_model_test.cc
index 6a8c15b..e9734a8 100644
--- a/vmec/ideal_mhd_model/ideal_mhd_model_test.cc
+++ b/vmec/ideal_mhd_model/ideal_mhd_model_test.cc
@@ -98,7 +98,7 @@ INSTANTIATE_TEST_SUITE_P(
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-30},
            DataSource{.identifier = "solovev_analytical", .tolerance = 1.0e-30},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-30},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-30},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-30, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-30},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-30},
@@ -178,7 +178,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMhdModel, FourierGeometryToStartWithTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-14},
@@ -342,7 +342,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, InverseFourierTransformGeometryTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 2.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 2.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 2.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 2.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 6.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 6.0e-14},
@@ -432,7 +432,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, JacobianTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 2.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 2.0e-14},
@@ -519,7 +519,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, MetricTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-15},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-15},
@@ -588,7 +588,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, VolumeTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-16},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-16},
@@ -722,7 +722,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ContravariantMagneticFieldTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-16},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-16},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-13},
@@ -798,7 +798,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, CovariantMagneticFieldTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 2.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 2.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-13},
@@ -881,7 +881,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, TotalPressureAndEnergiesTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-16},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-16},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-16},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-16, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-13},
@@ -972,7 +972,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, RadialForceBalanceTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-14},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-14},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-13},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-13, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-12},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-12},
@@ -1098,7 +1098,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, HybridLambdaForceTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-13},
@@ -1272,7 +1272,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, UpdateRadialPreconditionerTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-14},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-14},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-12},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-12},
@@ -1363,7 +1363,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ForceNormsTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-14},
@@ -1434,7 +1434,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ConstraintForceMultiplierTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 2.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 2.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-13},
@@ -1629,7 +1629,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, AliasTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-15, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 2.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 2.0e-14},
@@ -1738,7 +1738,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, RealspaceForcesTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-14},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-14},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-13},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-13, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-11},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-11},
@@ -1861,7 +1861,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ForwardTransformForcesTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-13},
@@ -1951,7 +1951,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, PhysicalForcesTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-13},
@@ -2012,7 +2012,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, InvariantResidualsTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-16},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-16},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-16},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-16, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-14},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-14},
@@ -2097,7 +2097,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ApplyM1PreconditionerTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 5.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-13},
@@ -2197,7 +2197,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, AssembleRZPreconditionerTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-14},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-14},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-12},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-12},
@@ -2363,7 +2363,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, ApplyPreconditionerTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-14},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-14},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-14, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-12},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-12},
@@ -2421,7 +2421,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestIdealMHDModel, PreconditionedResidualsTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 1.0e-16},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 1.0e-16},
-           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-16},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-16, .iter2_to_test = {1, 2, 3}},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 5.0e-16},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 5.0e-16},
diff --git a/vmec/vmec/vmec_test.cc b/vmec/vmec/vmec_test.cc
index ce0ef2c..45d6aaf 100644
--- a/vmec/vmec/vmec_test.cc
+++ b/vmec/vmec/vmec_test.cc
@@ -377,6 +377,7 @@ INSTANTIATE_TEST_SUITE_P(
     TestVmec, MultigridResultTest,
     Values(DataSource{.identifier = "solovev", .tolerance = 5.0e-15},
            DataSource{.identifier = "solovev_no_axis", .tolerance = 5.0e-15},
+           DataSource{.identifier = "solovev_free_bdy", .tolerance = 1.0e-11},
            DataSource{.identifier = "cth_like_fixed_bdy", .tolerance = 1.0e-13},
            DataSource{.identifier = "cth_like_fixed_bdy_nzeta_37",
                       .tolerance = 1.0e-13},