diff --git a/validphys2/src/validphys/tests/test_commondata_columns.py b/validphys2/src/validphys/tests/test_commondata_columns.py
deleted file mode 100644
index 157337edb1..0000000000
--- a/validphys2/src/validphys/tests/test_commondata_columns.py
+++ /dev/null
@@ -1,56 +0,0 @@
-"""
-Test that the multiplicative and additive columns of commondata
-are consistent.
-
-"""
-import numpy as np
-import pytest
-
-from validphys.commondataparser import load_commondata
-from validphys.loader import Loader
-
-def _cd_column_comparison(cd):
-    """Given a py:func:`validphys.coredata.CommonData` object, test
-    if the multiplicative and additive columns are consistent. In general
-    the ``mult`` columns and the ``add`` columns should be related by:
-
-        add = mult * central_value * 1e-2
-
-    """
-    add = cd.systematics_table.loc[:, ["ADD"]]
-    mult = cd.systematics_table.loc[:, ["MULT"]]
-    cv = cd.central_values
-    np.testing.assert_allclose(
-        cv.to_numpy()[:, np.newaxis] * mult.to_numpy() * 1e-2,
-        add.to_numpy(),
-        rtol=1e-05, # use the allclose values (less stringent tolerances)
-        atol=1e-08,
-    )
-
-DS_NAMES = [
-    "LHCBZEE2FB_40",
-    "LHCBW36PB_40",
-    "CDFZRAP_NEW",
-    "CMSTTBARTOT7TEV",
-    "CMSTTBARTOT8TEV",
-    "CMSTTBARTOT13TEV",
-    "CMS_2JET_3D_8TEV",
-    "D0ZRAP_40",
-    "ATLASPHT15",
-]
-
-L = Loader()
-
-@pytest.mark.parametrize("dataset_name", DS_NAMES)
-def test_dataset_commondata_columns_match(dataset_name):
-    """Apply :py:func:`_cd_column_comparison` to list of
-    datasets in ``DS_NAMES``. Checking if the columns in the
-    commondata file are self consistent.
-
-    """
-    # Note: If the dataset should have additional contributions to the
-    # covmat, like sys: 10 then DS_NAMES should be changed to be proper dataset
-    # inputs and we should use API here. Use loader to keep test fast.
-    cdspec = L.check_commondata(dataset_name)
-    lcd = load_commondata(cdspec)
-    _cd_column_comparison(lcd)
diff --git a/validphys2/src/validphys/tests/test_commondataparser.py b/validphys2/src/validphys/tests/test_commondataparser.py
index 92d115b434..7bf492ea76 100644
--- a/validphys2/src/validphys/tests/test_commondataparser.py
+++ b/validphys2/src/validphys/tests/test_commondataparser.py
@@ -4,22 +4,22 @@
 from validphys.api import API
 from validphys.commondataparser import load_commondata
 from validphys.loader import FallbackLoader as Loader
-from validphys.tests.conftest import THEORYID, FIT
+from validphys.tests.conftest import THEORYID_NEW, FIT
 
 
 def test_basic_commondata_loading():
     l = Loader()
-    cd = l.check_commondata(setname="H1HERAF2B")
+    cd = l.check_commondata(setname="SLAC_NC_NOTFIXED_D_DW_EM-F2", variant="legacy")
     res = load_commondata(cd)
     # Test commondata loading
-    assert res.ndata == 12
+    assert res.ndata == 211
     assert isinstance(res.commondata_table, pd.DataFrame)
     # Test systype loading
-    assert res.nsys == 25
+    assert res.nsys == 103
     assert isinstance(res.systype_table, pd.DataFrame)
 
     # Test a dataset with no systematics
-    emptysyscd = l.check_posset(theoryID=THEORYID, setname='POSDYCBD', postlambda=1e-10)
+    emptysyscd = l.check_posset(theoryID=THEORYID_NEW, setname='NNPDF_POS_2P24GEV_XDQ', postlambda=1e-10)
     emptysysres = load_commondata(emptysyscd.commondata)
     assert emptysysres.nsys == 0
     assert emptysysres.systype_table.empty is True
@@ -27,14 +27,14 @@ def test_basic_commondata_loading():
 
 def test_commondata_with_cuts():
     l = Loader()
-    setname = "NMC"
+    setname = "NMC_NC_NOTFIXED_P_EM-SIGMARED"
 
-    cd = l.check_commondata(setname=setname)
+    cd = l.check_commondata(setname=setname, variant="legacy")
     loaded_cd = load_commondata(cd)
 
     fit_cuts = l.check_fit_cuts(fit=FIT, commondata=cd)
     internal_cuts = l.check_internal_cuts(
-        cd, API.rules(theoryid=THEORYID, use_cuts="internal")
+        cd, API.rules(theoryid=THEORYID_NEW, use_cuts="internal")
     )
 
     loaded_cd_fit_cuts = loaded_cd.with_cuts(fit_cuts)
@@ -57,7 +57,7 @@ def test_commondata_with_cuts():
     assert all(loaded_cd.with_cuts([1, 2, 3]).commondata_table.index - 1 == [1, 2, 3])
 
     # Check that giving cuts for another dataset raises the correct ValueError exception
-    cd_bad = l.check_commondata(setname="NMCPD")
+    cd_bad = l.check_commondata(setname="NMC_NC_NOTFIXED_EM-F2", variant="legacy")
     bad_cuts = l.check_fit_cuts(fit=FIT, commondata=cd_bad)
     with pytest.raises(ValueError):
         loaded_cd.with_cuts(bad_cuts)