diff --git a/esmvalcore/cmor/_fixes/shared.py b/esmvalcore/cmor/_fixes/shared.py
index f6f4400dcd..fbace5d1e7 100644
--- a/esmvalcore/cmor/_fixes/shared.py
+++ b/esmvalcore/cmor/_fixes/shared.py
@@ -72,9 +72,7 @@ def add_plev_from_altitude(cube):
             pressure_bounds = altitude_to_pressure(height_coord.core_bounds())
         pressure_coord = iris.coords.AuxCoord(pressure_points,
                                               bounds=pressure_bounds,
-                                              var_name='plev',
                                               standard_name='air_pressure',
-                                              long_name='pressure',
                                               units='Pa')
         cube.add_aux_coord(pressure_coord, cube.coord_dims(height_coord))
         return
@@ -108,9 +106,7 @@ def add_altitude_from_plev(cube):
             altitude_bounds = pressure_to_altitude(plev_coord.core_bounds())
         altitude_coord = iris.coords.AuxCoord(altitude_points,
                                               bounds=altitude_bounds,
-                                              var_name='alt',
                                               standard_name='altitude',
-                                              long_name='altitude',
                                               units='m')
         cube.add_aux_coord(altitude_coord, cube.coord_dims(plev_coord))
         return
diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 800a035ab0..a724701beb 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -225,6 +225,12 @@ def _combine(cubes):
             coord.long_name = None
             coord.attributes = None
 
+        # Remove specific scalar coordinates which are not expected to be equal
+        scalar_coords_to_remove = ['p0', 'ptop']
+        for scalar_coord in cube.coords(dimensions=()):
+            if scalar_coord.var_name in scalar_coords_to_remove:
+                cube.remove_coord(scalar_coord)
+
     cubes = iris.cube.CubeList(cubes)
 
     merged_cube = cubes.merge_cube()
diff --git a/tests/integration/cmor/_fixes/test_common.py b/tests/integration/cmor/_fixes/test_common.py
index ace5cb5325..800ec736f5 100644
--- a/tests/integration/cmor/_fixes/test_common.py
+++ b/tests/integration/cmor/_fixes/test_common.py
@@ -156,9 +156,9 @@ def hybrid_height_coord_fix_metadata(nc_path, short_name, fix):
     air_pressure_coord = cube.coord('air_pressure')
     np.testing.assert_allclose(air_pressure_coord.points, PRESSURE_POINTS)
     np.testing.assert_allclose(air_pressure_coord.bounds, PRESSURE_BOUNDS)
-    assert air_pressure_coord.var_name == 'plev'
+    assert air_pressure_coord.var_name is None
     assert air_pressure_coord.standard_name == 'air_pressure'
-    assert air_pressure_coord.long_name == 'pressure'
+    assert air_pressure_coord.long_name is None
     assert air_pressure_coord.units == 'Pa'
 
 
diff --git a/tests/integration/cmor/_fixes/test_shared.py b/tests/integration/cmor/_fixes/test_shared.py
index 741c5e4233..a1a127066b 100644
--- a/tests/integration/cmor/_fixes/test_shared.py
+++ b/tests/integration/cmor/_fixes/test_shared.py
@@ -106,20 +106,15 @@ def test_add_aux_coords_from_cubes(coord_dict, output):
 
 
 ALT_COORD = iris.coords.AuxCoord([0.0], bounds=[[-100.0, 500.0]],
-                                 var_name='alt', long_name='altitude',
                                  standard_name='altitude', units='m')
-ALT_COORD_NB = iris.coords.AuxCoord([0.0], var_name='alt',
-                                    long_name='altitude',
-                                    standard_name='altitude', units='m')
+ALT_COORD_NB = iris.coords.AuxCoord([0.0], standard_name='altitude', units='m')
 ALT_COORD_KM = iris.coords.AuxCoord([0.0], bounds=[[-0.1, 0.5]],
                                     var_name='alt', long_name='altitude',
                                     standard_name='altitude', units='km')
 P_COORD = iris.coords.AuxCoord([101325.0], bounds=[[102532.0, 95460.8]],
-                               var_name='plev', standard_name='air_pressure',
-                               long_name='pressure', units='Pa')
-P_COORD_NB = iris.coords.AuxCoord([101325.0], var_name='plev',
-                                  standard_name='air_pressure',
-                                  long_name='pressure', units='Pa')
+                               standard_name='air_pressure', units='Pa')
+P_COORD_NB = iris.coords.AuxCoord([101325.0], standard_name='air_pressure',
+                                  units='Pa')
 CUBE_ALT = iris.cube.Cube([1.0], var_name='x',
                           aux_coords_and_dims=[(ALT_COORD, 0)])
 CUBE_ALT_NB = iris.cube.Cube([1.0], var_name='x',
diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index 7de15d6a0c..e15e0fd43b 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -8,6 +8,7 @@
 import numpy as np
 import pytest
 from cf_units import Unit
+from iris.coords import AuxCoord
 from iris.cube import Cube
 
 import esmvalcore.preprocessor._multimodel as mm
@@ -371,6 +372,25 @@ def test_combine_inconsistent_var_names_fail():
         _ = mm._combine(cubes)
 
 
+@pytest.mark.parametrize('scalar_coord', ['p0', 'ptop'])
+def test_combine_with_scalar_coords_to_remove(scalar_coord):
+    """Test _combine with scalar coordinates that should be removed."""
+    num_cubes = 5
+    cubes = []
+
+    for num in range(num_cubes):
+        cube = generate_cube_from_dates('monthly')
+        cubes.append(cube)
+
+    scalar_coord_0 = AuxCoord(0.0, var_name=scalar_coord)
+    scalar_coord_1 = AuxCoord(1.0, var_name=scalar_coord)
+    cubes[0].add_aux_coord(scalar_coord_0, ())
+    cubes[1].add_aux_coord(scalar_coord_1, ())
+
+    merged_cube = mm._combine(cubes)
+    assert merged_cube.shape == (5, 3)
+
+
 @pytest.mark.parametrize('span', SPAN_OPTIONS)
 def test_edge_case_different_time_offsets(span):
     cubes = (