diff --git a/pandas/tests/computation/test_eval.py b/pandas/tests/computation/test_eval.py
index 18559b9b4f899..86be104b16367 100644
--- a/pandas/tests/computation/test_eval.py
+++ b/pandas/tests/computation/test_eval.py
@@ -860,6 +860,19 @@ def test_basic_frame_series_alignment(
     def test_basic_series_frame_alignment(
         self, request, engine, parser, index_name, r_idx_type, c_idx_type
     ):
+        if (
+            engine == "numexpr"
+            and parser == "pandas"
+            and index_name == "index"
+            and r_idx_type == "i"
+            and c_idx_type == "s"
+        ):
+            reason = (
+                f"Flaky column ordering when engine={engine}, "
+                f"parser={parser}, index_name={index_name}, "
+                f"r_idx_type={r_idx_type}, c_idx_type={c_idx_type}"
+            )
+            request.node.add_marker(pytest.mark.xfail(reason=reason, strict=False))
         df = tm.makeCustomDataframe(
             10, 7, data_gen_f=f, r_idx_type=r_idx_type, c_idx_type=c_idx_type
         )
diff --git a/pandas/tests/io/test_clipboard.py b/pandas/tests/io/test_clipboard.py
index 5e4b2c1ebad9d..d018affdecfca 100644
--- a/pandas/tests/io/test_clipboard.py
+++ b/pandas/tests/io/test_clipboard.py
@@ -1,10 +1,15 @@
 import os
+import subprocess
 from textwrap import dedent
 
 import numpy as np
 import pytest
 
-from pandas.compat import is_platform_mac
+from pandas.compat import (
+    is_ci_environment,
+    is_platform_linux,
+    is_platform_mac,
+)
 from pandas.errors import (
     PyperclipException,
     PyperclipWindowsException,
@@ -409,6 +414,9 @@ def test_raw_roundtrip(self, data):
         # PR #25040 wide unicode wasn't copied correctly on PY3 on windows
         clipboard_set(data)
         assert data == clipboard_get()
+        if is_ci_environment() and is_platform_linux():
+            # Clipboard can sometimes keep previous param causing flaky CI failures
+            subprocess.run(["xsel", "--delete", "--clipboard"], check=True)
 
     @pytest.mark.parametrize("dtype_backend", ["pandas", "pyarrow"])
     @pytest.mark.parametrize("engine", ["c", "python"])