diff --git a/tests/config/test_configurable.py b/tests/config/test_configurable.py
index 4938e5ee..154af680 100644
--- a/tests/config/test_configurable.py
+++ b/tests/config/test_configurable.py
@@ -969,3 +969,9 @@ def test_logger_adapter(caplog, capsys):
     app.log.info("test message")
 
     assert "adapted test message" in capsys.readouterr().err
+
+
+def test_get_log_handler_deprecated():
+    app = Application(log=logging.getLogger("test_get_log_handler_deprecated"))
+    with pytest.deprecated_call(match="_get_log_handler has been deprecated"):
+        app._get_log_handler()
diff --git a/tests/config/test_loader.py b/tests/config/test_loader.py
index dcccb5a1..08fd6794 100644
--- a/tests/config/test_loader.py
+++ b/tests/config/test_loader.py
@@ -503,6 +503,14 @@ def test_auto_section(self):
         del c.A
         self.assertEqual(c.A, Config())
 
+    def test_has_key_deprecated(self):
+        c = Config()
+        c.a = 10
+        with pytest.deprecated_call(match="Config.has_key has been deprecated"):
+            assert c.has_key("a")
+        with pytest.deprecated_call(match="Config.has_key has been deprecated"):
+            assert not c.has_key("b")
+
     def test_merge_doesnt_exist(self):
         c1 = Config()
         c2 = Config()
diff --git a/tests/test_traitlets.py b/tests/test_traitlets.py
index 2e7b8459..968d034f 100644
--- a/tests/test_traitlets.py
+++ b/tests/test_traitlets.py
@@ -367,6 +367,17 @@ def test_trait_types_dict_deprecated(self):
             class C(HasTraits):
                 t = Dict(Int)
 
+    def test_no_default_specified_deprecated(self):
+        import traitlets.traitlets as tt
+
+        with expected_warnings(["NoDefaultSpecified is deprecated"]):
+            value = tt.NoDefaultSpecified
+        assert value is tt.Undefined
+        # still discoverable
+        assert "NoDefaultSpecified" in dir(tt)
+        with pytest.raises(AttributeError):
+            tt.this_does_not_exist
+
     def test_long_deprecated_aliases(self):
         for cls, replacement in [(Long, "Integer"), (CLong, "CInt")]:
             with expected_warnings([f"`{cls.__name__}` trait is deprecated"]):
diff --git a/traitlets/config/configurable.py b/traitlets/config/configurable.py
index 0bf7e23c..41efc1f3 100644
--- a/traitlets/config/configurable.py
+++ b/traitlets/config/configurable.py
@@ -506,9 +506,17 @@ def _get_log_handler(self) -> logging.Handler | None:
 
         Returns None if none can be found
 
-        Deprecated, this now returns the first log handler which may or may
-        not be the default one.
+        .. deprecated:: 5.2
+
+            This now returns the first log handler, which may or may not be
+            the default one. Use ``self.log.handlers`` directly instead.
         """
+        warnings.warn(
+            "Configurable._get_log_handler has been deprecated since traitlets 5.2 - 2022,"
+            " use the `.handlers` attribute of the logger directly.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
         if not self.log:
             return None
         logger: logging.Logger = (
diff --git a/traitlets/config/loader.py b/traitlets/config/loader.py
index 379cd479..33818e58 100644
--- a/traitlets/config/loader.py
+++ b/traitlets/config/loader.py
@@ -304,8 +304,15 @@ def __contains__(self, key: t.Any) -> bool:
 
         return super().__contains__(key)
 
-    # .has_key is deprecated for dictionaries.
-    has_key = __contains__
+    def has_key(self, key: t.Any) -> bool:
+        """Deprecated since traitlets 4.0 - 2015, use ``key in config`` instead."""
+        warnings.warn(
+            "Config.has_key has been deprecated since traitlets 4.0 - 2015,"
+            " use `key in config` instead.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        return self.__contains__(key)
 
     def _has_section(self, key: str) -> bool:
         return _is_section_key(key) and key in self
diff --git a/traitlets/traitlets.py b/traitlets/traitlets.py
index 0989ea98..1fe0d723 100644
--- a/traitlets/traitlets.py
+++ b/traitlets/traitlets.py
@@ -155,8 +155,31 @@
 """,
 )
 
-# Deprecated alias
-NoDefaultSpecified = Undefined
+# Deprecated aliases, kept accessible through the module-level ``__getattr__``
+# below so that reaching for them emits a DeprecationWarning (PEP 562).
+_deprecated_module_attrs = {
+    # name: (current name, message)
+    "NoDefaultSpecified": (
+        "Undefined",
+        (
+            "traitlets.traitlets.NoDefaultSpecified is deprecated since traitlets 4.0 - 2015,"
+            " use traitlets.Undefined instead."
+        ),
+    ),
+}
+
+
+def __getattr__(name: str) -> t.Any:
+    try:
+        target, msg = _deprecated_module_attrs[name]
+    except KeyError:
+        raise AttributeError(f"module {__name__!r} has no attribute {name!r}") from None
+    warn(msg, DeprecationWarning, stacklevel=2)
+    return globals()[target]
+
+
+def __dir__() -> list[str]:
+    return sorted([*globals(), *_deprecated_module_attrs])
 
 
 class TraitError(Exception):