diff --git a/py-polars/polars/dataframe/frame.py b/py-polars/polars/dataframe/frame.py
index cd59cc6bcdf7..79ea711ff14c 100644
--- a/py-polars/polars/dataframe/frame.py
+++ b/py-polars/polars/dataframe/frame.py
@@ -390,20 +390,6 @@ def __init__(
                 nan_to_null=nan_to_null,
             )
 
-        elif hasattr(data, "__arrow_c_array__"):
-            # This uses the fact that PySeries.from_arrow_c_array will create a
-            # struct-typed Series. Then we unpack that to a DataFrame.
-            tmp_col_name = ""
-            s = wrap_s(PySeries.from_arrow_c_array(data))
-            self._df = s.to_frame(tmp_col_name).unnest(tmp_col_name)._df
-
-        elif hasattr(data, "__arrow_c_stream__"):
-            # This uses the fact that PySeries.from_arrow_c_stream will create a
-            # struct-typed Series. Then we unpack that to a DataFrame.
-            tmp_col_name = ""
-            s = wrap_s(PySeries.from_arrow_c_stream(data))
-            self._df = s.to_frame(tmp_col_name).unnest(tmp_col_name)._df
-
         elif _check_for_pyarrow(data) and isinstance(data, pa.Table):
             self._df = arrow_to_pydf(
                 data, schema=schema, schema_overrides=schema_overrides, strict=strict
@@ -428,6 +414,21 @@ def __init__(
             self._df = dataframe_to_pydf(
                 data, schema=schema, schema_overrides=schema_overrides, strict=strict
             )
+
+        elif hasattr(data, "__arrow_c_array__"):
+            # This uses the fact that PySeries.from_arrow_c_array will create a
+            # struct-typed Series. Then we unpack that to a DataFrame.
+            tmp_col_name = ""
+            s = wrap_s(PySeries.from_arrow_c_array(data))
+            self._df = s.to_frame(tmp_col_name).unnest(tmp_col_name)._df
+
+        elif hasattr(data, "__arrow_c_stream__"):
+            # This uses the fact that PySeries.from_arrow_c_stream will create a
+            # struct-typed Series. Then we unpack that to a DataFrame.
+            tmp_col_name = ""
+            s = wrap_s(PySeries.from_arrow_c_stream(data))
+            self._df = s.to_frame(tmp_col_name).unnest(tmp_col_name)._df
+
         else:
             msg = (
                 f"DataFrame constructor called with unsupported type {type(data).__name__!r}"
diff --git a/py-polars/polars/series/series.py b/py-polars/polars/series/series.py
index 9a2badc28a86..42eaee869031 100644
--- a/py-polars/polars/series/series.py
+++ b/py-polars/polars/series/series.py
@@ -318,12 +318,6 @@ def __init__(
             if dtype is not None:
                 self._s = self.cast(dtype, strict=strict)._s
 
-        elif hasattr(values, "__arrow_c_array__"):
-            self._s = PySeries.from_arrow_c_array(values)
-
-        elif hasattr(values, "__arrow_c_stream__"):
-            self._s = PySeries.from_arrow_c_stream(values)
-
         elif _check_for_pyarrow(values) and isinstance(
             values, (pa.Array, pa.ChunkedArray)
         ):
@@ -347,6 +341,12 @@ def __init__(
                 original_name, values, dtype=dtype, strict=strict
             )
 
+        elif hasattr(values, "__arrow_c_array__"):
+            self._s = PySeries.from_arrow_c_array(values)
+
+        elif hasattr(values, "__arrow_c_stream__"):
+            self._s = PySeries.from_arrow_c_stream(values)
+
         else:
             msg = (
                 f"Series constructor called with unsupported type {type(values).__name__!r}"