diff --git a/cf_xarray/datasets.py b/cf_xarray/datasets.py
index facefa1e..f2483860 100644
--- a/cf_xarray/datasets.py
+++ b/cf_xarray/datasets.py
@@ -129,6 +129,7 @@
 # fmt: on
 romsds.coords["hc"] = 20.0
 romsds.coords["h"] = 603.9
+romsds.h.attrs["standard_name"] = "sea_floor_depth_below_geopotential_datum"
 romsds.coords["Vtransform"] = 2.0
 # fmt: off
 romsds.coords["Cs_r"] = (
@@ -143,7 +144,11 @@
      -5.20560097e-04, -5.75774004e-05],
 )
 # fmt: on
-romsds["zeta"] = ("ocean_time", [-0.155356, -0.127435])
+romsds["zeta"] = (
+    "ocean_time",
+    [-0.155356, -0.127435],
+    {"standard_name": "sea_surface_height_above_geopotential_datum"},
+)
 romsds["temp"] = (
     ("ocean_time", "s_rho"),
     [np.linspace(20, 30, 30)] * 2,
diff --git a/cf_xarray/tests/test_accessor.py b/cf_xarray/tests/test_accessor.py
index 225bab8c..6657be46 100644
--- a/cf_xarray/tests/test_accessor.py
+++ b/cf_xarray/tests/test_accessor.py
@@ -1785,10 +1785,8 @@ def test_decode_vertical_coords() -> None:
     # Fixes 'UnboundLocalError: cannot access local variable 'romsds' where it is not associated with a value'
     from ..datasets import romsds
 
-    # needs standard names on `eta` and `depth` to derive computed standard name
-    romsds.h.attrs["standard_name"] = "sea_floor_depth_below_geopotential_datum"
-    romsds.zeta.attrs["standard_name"] = "sea_surface_height_above_geopotential_datum"
-
+    # romsds already carries standard names on `eta` and `depth`, so the
+    # computed standard name can be derived without any extra setup.
     romsds.cf.decode_vertical_coords(outnames={"s_rho": "z_rho"})
 
     assert romsds.z_rho.shape == (2, 30)