diff --git a/esmvalcore/cmor/_fixes/emac/_base_fixes.py b/esmvalcore/cmor/_fixes/emac/_base_fixes.py
index 5082f612c9..5f9428258c 100644
--- a/esmvalcore/cmor/_fixes/emac/_base_fixes.py
+++ b/esmvalcore/cmor/_fixes/emac/_base_fixes.py
@@ -38,11 +38,8 @@ def get_cube(self, cubes, var_name=None):
         raise ValueError(
             f"No variable of {var_names} necessary for the extraction/"
             f"derivation the CMOR variable '{self.vardef.short_name}' is "
-            f"available in the input file. Hint: in case you tried to extract "
-            f"a 3D variable defined on pressure levels, it might be necessary "
-            f"to define the EMAC variable name in the recipe (e.g., "
-            f"'raw_name: tm1_p39_cav') if the default number of pressure "
-            f"levels is not available in the input file."
+            f"available in the input file. Please specify a valid `raw_name` "
+            f"in the recipe or extra facets file."
         )
 
 
diff --git a/esmvalcore/config/extra_facets/emac-mappings.yml b/esmvalcore/config/extra_facets/emac-mappings.yml
index 3e98cd2ba4..5efd0edab4 100644
--- a/esmvalcore/config/extra_facets/emac-mappings.yml
+++ b/esmvalcore/config/extra_facets/emac-mappings.yml
@@ -11,14 +11,15 @@
 #   latter case, the prioritization is given by the order of the list; if
 #   possible, use the first entry, if this is not present, use the second, etc.
 #   This is particularly useful for variables where regular averages ("*_ave")
-#   or conditional averages ("*_cav") exist. For 3D variables defined on
-#   pressure levels, only the pressure levels defined by the CMOR table (e.g.,
-#   for Amon's ta: "tm1_p19_cav" and "tm1_p19_ave") are given. If other
-#   pressure levels are desired, e.g., "tm1_p39_cav", this has to be explicitly
-#   specified in the recipe using "raw_name: tm1_p39_cav" or "raw_name:
-#   [tm1_p19_cav, tm1_p39_cav]".
+#   or conditional averages ("*_cav") exist. If other variables are desired,
+#   e.g., "tm1_p39_cav", this has to be explicitly specified in the recipe
+#   ("raw_name: tm1_p39_cav".)
 # - Asterisks ("*") in the comments in list below refer to either "cav" or
 #   "ave". "cav" is prioritized.
+# - The channels given here are generalization and may not always be
+#   applicable. In that case choose the channels with the appropriate variable
+#   per recipe.
+#
 
 # A complete list of supported keys is given in the documentation (see
 # ESMValCore/doc/quickstart/find_data.rst).
@@ -35,71 +36,71 @@ EMAC:
   # 1D/2D dynamical/meteorological variables
   '*':
     awhea:  # non-CMOR variable
-      raw_name: [awhea_cav, awhea_ave]
+      raw_name: [awhea_cav, awhea_ave, awhea]
       channel: Omon
     clivi:
-      raw_name: [xivi_cav, xivi_ave]
+      raw_name: [xivi_cav, xivi_ave, xivi]
       channel: Amon
     clt:
-      raw_name: [aclcov_cav, aclcov_ave]
+      raw_name: [aclcov_cav, aclcov_ave, aclcov]
       raw_units: '1'
       channel: Amon
     clwvi:  # derived from xlvi_*, xivi_*
       channel: Amon
     co2mass:
-      raw_name: [MP_CO2_cav, MP_CO2_ave]
+      raw_name: [MP_CO2_cav, MP_CO2_ave, MP_CO2]
       channel: tracer_pdef_gp
     evspsbl:
-      raw_name: [evap_cav, evap_ave]
+      raw_name: [evap_cav, evap_ave, evap]
       channel: Amon
     hfls:
-      raw_name: [ahfl_cav, ahfl_ave]
+      raw_name: [ahfl_cav, ahfl_ave, ahfl]
       channel: Amon
     hfns:  # ESMValCore-derivation
       channel: Amon
     hfss:
-      raw_name: [ahfs_cav, ahfs_ave]
+      raw_name: [ahfs_cav, ahfs_ave, ahfs]
       channel: Amon
     hurs:
-      raw_name: [rh_2m_cav, rh_2m_ave]
+      raw_name: [rh_2m_cav, rh_2m_ave, rh_2m]
       raw_units: '1'
       channel: Amon
     od550aer:
-      raw_name: [aot_opt_TOT_550_total_cav, aot_opt_TOT_550_total_ave]
+      raw_name: [aot_opt_TOT_550_total_cav, aot_opt_TOT_550_total_ave, aot_opt_TOT_550_total]
       raw_units: '1'
       channel: AERmon
     pr:  # derived from aprl_*, aprc_*
       channel: Amon
     prc:
-      raw_name: [aprc_cav, aprc_ave]
+      raw_name: [aprc_cav, aprc_ave, aprc]
       channel: Amon
     prl:  # non-CMOR variable
-      raw_name: [aprl_cav, aprl_ave]
+      raw_name: [aprl_cav, aprl_ave, aprl]
       channel: Amon
     prsn:
-      raw_name: [aprs_cav, aprs_ave]
+      raw_name: [aprs_cav, aprs_ave, aprs]
       channel: Amon
     prw:
-      raw_name: [qvi_cav, qvi_ave]
+      raw_name: [qvi_cav, qvi_ave, qvi]
       channel: Amon
     ps:
-      raw_name: [aps_cav, aps_ave]
+      raw_name: [aps_cav, aps_ave, aps]
       channel: Amon
     psl:
-      raw_name: [slp_cav, slp_ave]
+      raw_name: [slp_cav, slp_ave, slp]
       channel: Amon
     rlds:  # derived from flxtbot_*, tradsu_*
       channel: Amon
     rlns:  # ESMValCore-derivation
       channel: Amon
     rlus:
-      raw_name: [tradsu_cav, tradsu_ave]
+      raw_name: [tradsu_cav, tradsu_ave, tradsu]
       channel: Amon
     rlut:
-      raw_name: [flxttop_cav, flxttop_ave]
+      raw_name: [flxttop_cav, flxttop_ave, flxttop]
       channel: Amon
     rlutcs:
-      raw_name: [flxtftop_cav, flxtftop_ave]
+      raw_name: [flxtftop_cav, flxtftop_ave, flxtftop]
       channel: Amon
     rsds:  # derived from flxsbot_*, sradsu_*
       channel: Amon
@@ -110,32 +111,32 @@ EMAC:
     rsnt:  # ESMValCore-derivation
       channel: Amon
     rsus:
-      raw_name: [sradsu_cav, sradsu_ave]
+      raw_name: [sradsu_cav, sradsu_ave, sradsu]
       channel: Amon
     rsut:
-      raw_name: [srad0u_cav, srad0u_ave]
+      raw_name: [srad0u_cav, srad0u_ave, srad0u]
       channel: Amon
     rsutcs:
-      raw_name: [flxusftop_cav, flxusftop_ave]
+      raw_name: [flxusftop_cav, flxusftop_ave, flxusftop]
       channel: Amon
     rtmt:  # derived from flxttop_*, flxstop_*
       channel: Amon
     sfcWind:
-      raw_name: [wind10_cav, wind10_ave]
+      raw_name: [wind10_cav, wind10_ave, wind10]
       channel: Amon
     siconc:
-      raw_name: [seaice_cav, seaice_ave]
+      raw_name: [seaice_cav, seaice_ave, seaice]
       raw_units: '1'
       channel: Amon
     siconca:
-      raw_name: [seaice_cav, seaice_ave]
+      raw_name: [seaice_cav, seaice_ave, seaice]
       raw_units: '1'
       channel: Amon
     sithick:
-      raw_name: [siced_cav, siced_ave]
+      raw_name: [siced_cav, siced_ave, siced]
       channel: Amon
     tas:
-      raw_name: [temp2_cav, temp2_ave]
+      raw_name: [temp2_cav, temp2_ave, temp2]
       channel: Amon
     tasmax:
       raw_name: temp2_max
@@ -144,10 +145,10 @@ EMAC:
       raw_name: temp2_min
       channel: Amon
     tauu:
-      raw_name: [ustr_cav, ustr_ave]
+      raw_name: [ustr_cav, ustr_ave, ustr]
       channel: Amon
     tauv:
-      raw_name: [vstr_cav, vstr_ave]
+      raw_name: [vstr_cav, vstr_ave, vstr]
       channel: Amon
     tos:
       raw_name: tsw
@@ -155,210 +156,99 @@ EMAC:
     toz:
       channel: column
     ts:
-      raw_name: [tsurf_cav, tsurf_ave]
+      raw_name: [tsurf_cav, tsurf_ave, tsurf]
       channel: Amon
     uas:
-      raw_name: [u10_cav, u10_ave]
+      raw_name: [u10_cav, u10_ave, u10]
       channel: Amon
     vas:
-      raw_name: [v10_cav, v10_ave]
+      raw_name: [v10_cav, v10_ave, v10]
       channel: Amon
 
     # Tracers (non-CMOR variables)
     MP_BC_tot:  # derived from MP_BC_ks_*, MP_BC_as_*, MP_BC_cs_*, MP_BC_ki_*
       channel: tracer_pdef_gp
     MP_CFCl3:
-      raw_name: [MP_CFCl3_cav, MP_CFCl3_ave]
+      raw_name: [MP_CFCl3_cav, MP_CFCl3_ave, MP_CFCl3]
       channel: tracer_pdef_gp
     MP_ClOX:
-      raw_name: [MP_ClOX_cav, MP_ClOX_ave]
+      raw_name: [MP_ClOX_cav, MP_ClOX_ave, MP_ClOX]
       channel: tracer_pdef_gp
     MP_CH4:
-      raw_name: [MP_CH4_cav, MP_CH4_ave]
+      raw_name: [MP_CH4_cav, MP_CH4_ave, MP_CH4]
       channel: tracer_pdef_gp
     MP_CO:
-      raw_name: [MP_CO_cav, MP_CO_ave]
+      raw_name: [MP_CO_cav, MP_CO_ave, MP_CO]
       channel: tracer_pdef_gp
     MP_CO2:
-      raw_name: [MP_CO2_cav, MP_CO2_ave]
+      raw_name: [MP_CO2_cav, MP_CO2_ave, MP_CO2]
       channel: tracer_pdef_gp
     MP_DU_tot:  # derived from MP_DU_as_*, MP_DU_cs_*, MP_DU_ai_*, MP_DU_ci_*
       channel: tracer_pdef_gp
     MP_N2O:
-      raw_name: [MP_N2O_cav, MP_N2O_ave]
+      raw_name: [MP_N2O_cav, MP_N2O_ave, MP_N2O]
       channel: tracer_pdef_gp
     MP_NH3:
-      raw_name: [MP_NH3_cav, MP_NH3_ave]
+      raw_name: [MP_NH3_cav, MP_NH3_ave, MP_NH3]
       channel: tracer_pdef_gp
     MP_NO:
-      raw_name: [MP_NO_cav, MP_NO_ave]
+      raw_name: [MP_NO_cav, MP_NO_ave, MP_NO]
       channel: tracer_pdef_gp
     MP_NO2:
-      raw_name: [MP_NO2_cav, MP_NO2_ave]
+      raw_name: [MP_NO2_cav, MP_NO2_ave, MP_NO2]
       channel: tracer_pdef_gp
     MP_NOX:
-      raw_name: [MP_NOX_cav, MP_NOX_ave]
+      raw_name: [MP_NOX_cav, MP_NOX_ave, MP_NOX]
       channel: tracer_pdef_gp
     MP_O3:
-      raw_name: [MP_O3_cav, MP_O3_ave]
+      raw_name: [MP_O3_cav, MP_O3_ave, MP_O3]
       channel: tracer_pdef_gp
     MP_OH:
-      raw_name: [MP_OH_cav, MP_OH_ave]
+      raw_name: [MP_OH_cav, MP_OH_ave, MP_OH]
       channel: tracer_pdef_gp
     MP_S:
-      raw_name: [MP_S_cav, MP_S_ave]
+      raw_name: [MP_S_cav, MP_S_ave, MP_S]
       channel: tracer_pdef_gp
     MP_SO2:
-      raw_name: [MP_SO2_cav, MP_SO2_ave]
+      raw_name: [MP_SO2_cav, MP_SO2_ave, MP_SO2]
       channel: tracer_pdef_gp
     MP_SO4mm_tot:  # derived from MP_SO4mm_ns_*, MP_SO4mm_ks_*, MP_SO4mm_as_*, MP_SO4mm_cs_*
       channel: tracer_pdef_gp
     MP_SS_tot:  # derived from MP_SS_ks_*, MP_SS_as_*, MP_SS_cs_*
       channel: tracer_pdef_gp
 
-  # 3D dynamical/meteorological variables
-  6hrLev:
-    ta:
-      raw_name: [tm1_cav, tm1_ave]
-      channel: Amon
-    ua:
-      raw_name: [um1_cav, um1_ave]
-      channel: Amon
-    va:
-      raw_name: [vm1_cav, vm1_ave]
-      channel: Amon
-  AERmon:
-    ua:
-      raw_name: [um1_cav, um1_ave]
-      channel: Amon
-    va:
-      raw_name: [vm1_cav, vm1_ave]
-      channel: Amon
-    zg:
-      raw_name: [geopot_cav, geopot_ave]
-      channel: Amon
-  Amon:
-    cl:
-      raw_name: [aclcac_cav, aclcac_ave]
-      raw_units: '1'
-      channel: Amon
-    cli:
-      raw_name: [xim1_cav, xim1_ave]
-      channel: Amon
-    clw:
-      raw_name: [xlm1_cav, xlm1_ave]
-      channel: Amon
-    hur:  # defined on plev19
-      raw_name: [rhum_p19_cav, rhum_p19_ave]
-      channel: Amon
-    hus:  # defined on plev19
-      raw_name: [qm1_p19_cav, qm1_p19_ave]
-      channel: Amon
-    ta:  # defined on plev19
-      raw_name: [tm1_p19_cav, tm1_p19_ave]
-      channel: Amon
-    ua:  # defined on plev19
-      raw_name: [um1_p19_cav, um1_p19_ave]
-      channel: Amon
-    va:  # defined on plev19
-      raw_name: [vm1_p19_cav, vm1_p19_ave]
-      channel: Amon
-    zg:  # defined on plev19
-      raw_name: [geopot_p19_cav, geopot_p19_ave]
-      channel: Amon
-  CF3hr:
-    ta:
-      raw_name: [tm1_cav, tm1_ave]
-      channel: Amon
-  CFday:
+    # 3D dynamical/meteorological variables
     cl:
-      raw_name: [aclcac_cav, aclcac_ave]
+      raw_name: [aclcac_cav, aclcac_ave, aclcac]
       raw_units: '1'
       channel: Amon
     cli:
-      raw_name: [xim1_cav, xim1_ave]
+      raw_name: [xim1_cav, xim1_ave, xim1]
       channel: Amon
     clw:
-      raw_name: [xlm1_cav, xlm1_ave]
+      raw_name: [xlm1_cav, xlm1_ave, xlm1]
       channel: Amon
     hur:
-      raw_name: [rhum_cav, rhum_ave]
+      raw_name: [rhum_cav, rhum_ave, rhum]
       channel: Amon
     hus:
-      raw_name: [qm1_cav, qm1_ave]
+      raw_name: [qm1_cav, qm1_ave, qm1]
       channel: Amon
-    ta:
-      raw_name: [tm1_cav, tm1_ave]
-      channel: Amon
-    ua:
-      raw_name: [um1_cav, um1_ave]
-      channel: Amon
-    va:
-      raw_name: [vm1_cav, vm1_ave]
-      channel: Amon
-    zg:
-      raw_name: [geopot_cav, geopot_ave]
-      channel: Amon
-  CFmon:
-    hur:
-      raw_name: [rhum_cav, rhum_ave]
-      channel: Amon
-    hus:
-      raw_name: [qm1_cav, qm1_ave]
+    o3:
+      raw_name: [O3_cav, O3_ave, O3]
       channel: Amon
     ta:
-      raw_name: [tm1_cav, tm1_ave]
-      channel: Amon
-  day:
-    hur:  # defined on plev8
-      raw_name: [rhum_p8_cav, rhum_p8_ave]
-      channel: Amon
-    hus:  # defined on plev8
-      raw_name: [qm1_p8_cav, qm1_p8_ave]
-      channel: Amon
-    ua:  # defined on plev8
-      raw_name: [um1_p8_cav, um1_p8_ave]
-      channel: Amon
-    va:  # defined on plev8
-      raw_name: [vm1_p8_cav, vm1_p8_ave]
+      raw_name: [tm1_cav, tm1_ave, tm1]
       channel: Amon
-    zg:  # defined on plev8
-      raw_name: [geopot_p8_cav, geopot_p8_ave]
-      channel: Amon
-  E1hr:
-    ua:  # defined on plev3
-      raw_name: [um1_p3_cav, um1_p3_ave]
-      channel: Amon
-    va: # defined on plev3
-      raw_name: [vm1_p3_cav, vm1_p3_ave]
-      channel: Amon
-  E3hrPt:
-    hus:
-      raw_name: [qm1_cav, qm1_ave]
-      channel: Amon
-  Eday:
-    ta:  # defined on plev19
-      raw_name: [tm1_p19_cav, tm1_p19_ave]
-      channel: Amon
-    hus:  # defined on plev19
-      raw_name: [qm1_p19_cav, qm1_p19_ave]
-      channel: Amon
-    ua:  # defined on plev19
-      raw_name: [um1_p19_cav, um1_p19_ave]
-      channel: Amon
-    va:  # defined on plev19
-      raw_name: [vm1_p19_cav, vm1_p19_ave]
-      channel: Amon
-    zg:  # defined on plev19
-      raw_name: [geopot_p19_cav, geopot_p19_ave]
-      channel: Amon
-  Esubhr:
-    ta:
-      raw_name: [tm1_cav, tm1_ave]
+    tro3:
+      raw_name: [O3_cav, O3_ave, O3]
       channel: Amon
     ua:
-      raw_name: [um1_cav, um1_ave]
+      raw_name: [um1_cav, um1_ave, um1]
       channel: Amon
     va:
-      raw_name: [vm1_cav, vm1_ave]
+      raw_name: [vm1_cav, vm1_ave, vm1]
+      channel: Amon
+    zg:
+      raw_name: [geopot_cav, geopot_ave, geopot]
       channel: Amon
diff --git a/tests/integration/cmor/_fixes/emac/test_emac.py b/tests/integration/cmor/_fixes/emac/test_emac.py
index 1146502a42..8376b865d4 100644
--- a/tests/integration/cmor/_fixes/emac/test_emac.py
+++ b/tests/integration/cmor/_fixes/emac/test_emac.py
@@ -538,7 +538,7 @@ def test_var_not_available_fix():
     """Test fix."""
     fix = get_allvars_fix('Amon', 'ta')
     cubes = CubeList([Cube(0.0)])
-    msg = (r"No variable of \['tm1_p19_cav', 'tm1_p19_ave'\] necessary for "
+    msg = (r"No variable of \['tm1_cav', 'tm1_ave', 'tm1'\] necessary for "
            r"the extraction/derivation the CMOR variable 'ta' is available in "
            r"the input file.")
     with pytest.raises(ValueError, match=msg):
@@ -577,7 +577,7 @@ def test_only_time(monkeypatch):
                           units='days since 1850-01-01')
     cubes = CubeList([
         Cube([1, 1],
-             var_name='tm1_p19_ave',
+             var_name='tm1_cav',
              units='K',
              dim_coords_and_dims=[(time_coord, 0)]),
     ])
@@ -622,7 +622,7 @@ def test_only_plev(monkeypatch):
                           units='hPa')
     cubes = CubeList([
         Cube([1, 1],
-             var_name='tm1_p19_ave',
+             var_name='tm1_ave',
              units='K',
              dim_coords_and_dims=[(plev_coord, 0)]),
     ])
@@ -667,7 +667,7 @@ def test_only_latitude(monkeypatch):
                          units='degrees')
     cubes = CubeList([
         Cube([1, 1],
-             var_name='tm1_p19_ave',
+             var_name='tm1',
              units='K',
              dim_coords_and_dims=[(lat_coord, 0)]),
     ])
@@ -712,7 +712,7 @@ def test_only_longitude(monkeypatch):
                          units='degrees')
     cubes = CubeList([
         Cube([1, 1],
-             var_name='tm1_p19_ave',
+             var_name='tm1',
              units='K',
              dim_coords_and_dims=[(lon_coord, 0)]),
     ])
@@ -2438,7 +2438,7 @@ def test_get_hur_fix():
 
 def test_hur_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'rhum_p19_cav'
+    cubes_3d[0].var_name = 'rhum_cav'
     cubes_3d[0].units = '1'
     fix = get_allvars_fix('Amon', 'hur')
     fixed_cubes = fix.fix_metadata(cubes_3d)
@@ -2465,7 +2465,7 @@ def test_get_hus_fix():
 
 def test_hus_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'qm1_p19_cav'
+    cubes_3d[0].var_name = 'qm1_cav'
     cubes_3d[0].units = '1'
     fix = get_allvars_fix('Amon', 'hus')
     fixed_cubes = fix.fix_metadata(cubes_3d)
@@ -2492,7 +2492,7 @@ def test_get_ta_fix():
 
 def test_ta_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'tm1_p19_cav'
+    cubes_3d[0].var_name = 'tm1_cav'
     cubes_3d[0].units = 'K'
     fix = get_allvars_fix('Amon', 'ta')
     fixed_cubes = fix.fix_metadata(cubes_3d)
@@ -2519,7 +2519,7 @@ def test_get_ua_fix():
 
 def test_ua_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'um1_p19_cav'
+    cubes_3d[0].var_name = 'um1_cav'
     cubes_3d[0].units = 'm s-1'
     fix = get_allvars_fix('Amon', 'ua')
     fixed_cubes = fix.fix_metadata(cubes_3d)
@@ -2546,7 +2546,7 @@ def test_get_va_fix():
 
 def test_va_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'vm1_p19_cav'
+    cubes_3d[0].var_name = 'vm1_cav'
     cubes_3d[0].units = 'm s-1'
     fix = get_allvars_fix('Amon', 'va')
     fixed_cubes = fix.fix_metadata(cubes_3d)
@@ -2573,7 +2573,7 @@ def test_get_zg_fix():
 
 def test_zg_fix(cubes_3d):
     """Test fix."""
-    cubes_3d[0].var_name = 'geopot_p19_cav'
+    cubes_3d[0].var_name = 'geopot_cav'
     cubes_3d[0].units = 'm2 s-2'
     fix = get_fix('Amon', 'zg')
     fixed_cubes = fix.fix_metadata(cubes_3d)