diff --git a/xarray/coding/strings.py b/xarray/coding/strings.py
index 89ceaddd93b..fa57bffb8d5 100644
--- a/xarray/coding/strings.py
+++ b/xarray/coding/strings.py
@@ -47,12 +47,11 @@ class EncodedStringCoder(VariableCoder):
     def __init__(self, allows_unicode=True):
         self.allows_unicode = allows_unicode
 
-    def encode(self, variable, name=None):
+    def encode(self, variable: Variable, name=None) -> Variable:
         dims, data, attrs, encoding = unpack_for_encoding(variable)
 
         contains_unicode = is_unicode_dtype(data.dtype)
         encode_as_char = encoding.get("dtype") == "S1"
-
         if encode_as_char:
             del encoding["dtype"]  # no longer relevant
 
@@ -69,9 +68,12 @@ def encode(self, variable, name=None):
             # TODO: figure out how to handle this in a lazy way with dask
             data = encode_string_array(data, string_encoding)
 
-        return Variable(dims, data, attrs, encoding)
+            return Variable(dims, data, attrs, encoding)
+        else:
+            variable.encoding = encoding
+            return variable
 
-    def decode(self, variable, name=None):
+    def decode(self, variable: Variable, name=None) -> Variable:
         dims, data, attrs, encoding = unpack_for_decoding(variable)
 
         if "_Encoding" in attrs:
@@ -95,13 +97,15 @@ def encode_string_array(string_array, encoding="utf-8"):
     return np.array(encoded, dtype=bytes).reshape(string_array.shape)
 
 
-def ensure_fixed_length_bytes(var):
+def ensure_fixed_length_bytes(var: Variable) -> Variable:
     """Ensure that a variable with vlen bytes is converted to fixed width."""
-    dims, data, attrs, encoding = unpack_for_encoding(var)
-    if check_vlen_dtype(data.dtype) == bytes:
+    if check_vlen_dtype(var.dtype) == bytes:
+        dims, data, attrs, encoding = unpack_for_encoding(var)
         # TODO: figure out how to handle this with dask
         data = np.asarray(data, dtype=np.bytes_)
-    return Variable(dims, data, attrs, encoding)
+        return Variable(dims, data, attrs, encoding)
+    else:
+        return var
 
 
 class CharacterArrayCoder(VariableCoder):
diff --git a/xarray/conventions.py b/xarray/conventions.py
index 8c7d6be2309..bf9f315c326 100644
--- a/xarray/conventions.py
+++ b/xarray/conventions.py
@@ -16,7 +16,7 @@
 )
 from xarray.core.pycompat import is_duck_dask_array
 from xarray.core.utils import emit_user_level_warning
-from xarray.core.variable import IndexVariable, Variable
+from xarray.core.variable import Variable
 
 CF_RELATED_DATA = (
     "bounds",
@@ -97,10 +97,10 @@ def _infer_dtype(array, name=None):
 
 
 def ensure_not_multiindex(var: Variable, name: T_Name = None) -> None:
-    if isinstance(var, IndexVariable) and isinstance(var.to_index(), pd.MultiIndex):
+    if isinstance(var._data, indexing.PandasMultiIndexingAdapter):
         raise NotImplementedError(
             f"variable {name!r} is a MultiIndex, which cannot yet be "
-            "serialized to netCDF files. Instead, either use reset_index() "
+            "serialized. Instead, either use reset_index() "
             "to convert MultiIndex levels into coordinate variables instead "
             "or use https://cf-xarray.readthedocs.io/en/latest/coding.html."
         )
@@ -647,7 +647,9 @@ def cf_decoder(
     return variables, attributes
 
 
-def _encode_coordinates(variables, attributes, non_dim_coord_names):
+def _encode_coordinates(
+    variables: T_Variables, attributes: T_Attrs, non_dim_coord_names
+):
     # calculate global and variable specific coordinates
     non_dim_coord_names = set(non_dim_coord_names)
 
@@ -675,7 +677,7 @@ def _encode_coordinates(variables, attributes, non_dim_coord_names):
                 variable_coordinates[k].add(coord_name)
 
             if any(
-                attr_name in v.encoding and coord_name in v.encoding.get(attr_name)
+                coord_name in v.encoding.get(attr_name, tuple())
                 for attr_name in CF_RELATED_DATA
             ):
                 not_technically_coordinates.add(coord_name)
@@ -742,7 +744,7 @@ def _encode_coordinates(variables, attributes, non_dim_coord_names):
     return variables, attributes
 
 
-def encode_dataset_coordinates(dataset):
+def encode_dataset_coordinates(dataset: Dataset):
     """Encode coordinates on the given dataset object into variable specific
     and global attributes.
 
@@ -764,7 +766,7 @@ def encode_dataset_coordinates(dataset):
     )
 
 
-def cf_encoder(variables, attributes):
+def cf_encoder(variables: T_Variables, attributes: T_Attrs):
     """
     Encode a set of CF encoded variables and attributes.
     Takes a dicts of variables and attributes and encodes them
diff --git a/xarray/tests/test_coding_times.py b/xarray/tests/test_coding_times.py
index 94d3ea92af2..b9190fb4252 100644
--- a/xarray/tests/test_coding_times.py
+++ b/xarray/tests/test_coding_times.py
@@ -733,7 +733,7 @@ def test_encode_time_bounds() -> None:
 
     # if time_bounds attrs are same as time attrs, it doesn't matter
     ds.time_bounds.encoding = {"calendar": "noleap", "units": "days since 2000-01-01"}
-    encoded, _ = cf_encoder({k: ds[k] for k in ds.variables}, ds.attrs)
+    encoded, _ = cf_encoder({k: v for k, v in ds.variables.items()}, ds.attrs)
     assert_equal(encoded["time_bounds"], expected["time_bounds"])
     assert "calendar" not in encoded["time_bounds"].attrs
     assert "units" not in encoded["time_bounds"].attrs
@@ -741,7 +741,7 @@ def test_encode_time_bounds() -> None:
     # for CF-noncompliant case of time_bounds attrs being different from
     # time attrs; preserve them for faithful roundtrip
     ds.time_bounds.encoding = {"calendar": "noleap", "units": "days since 1849-01-01"}
-    encoded, _ = cf_encoder({k: ds[k] for k in ds.variables}, ds.attrs)
+    encoded, _ = cf_encoder({k: v for k, v in ds.variables.items()}, ds.attrs)
     with pytest.raises(AssertionError):
         assert_equal(encoded["time_bounds"], expected["time_bounds"])
     assert "calendar" not in encoded["time_bounds"].attrs