diff --git a/asv_bench/benchmarks/tslibs/timestamp.py b/asv_bench/benchmarks/tslibs/timestamp.py
index 8ebb2d8d2f35d..3ef9b814dd79e 100644
--- a/asv_bench/benchmarks/tslibs/timestamp.py
+++ b/asv_bench/benchmarks/tslibs/timestamp.py
@@ -1,12 +1,19 @@
 import datetime
 
 import dateutil
+import numpy as np
 import pytz
 
 from pandas import Timestamp
 
 
 class TimestampConstruction:
+    def setup(self):
+        self.npdatetime64 = np.datetime64("2020-01-01 00:00:00")
+        self.dttime_unaware = datetime.datetime(2020, 1, 1, 0, 0, 0)
+        self.dttime_aware = datetime.datetime(2020, 1, 1, 0, 0, 0, 0, pytz.UTC)
+        self.ts = Timestamp("2020-01-01 00:00:00")
+
     def time_parse_iso8601_no_tz(self):
         Timestamp("2017-08-25 08:16:14")
 
@@ -28,6 +35,18 @@ def time_fromordinal(self):
     def time_fromtimestamp(self):
         Timestamp.fromtimestamp(1515448538)
 
+    def time_from_npdatetime64(self):
+        Timestamp(self.npdatetime64)
+
+    def time_from_datetime_unaware(self):
+        Timestamp(self.dttime_unaware)
+
+    def time_from_datetime_aware(self):
+        Timestamp(self.dttime_aware)
+
+    def time_from_pd_timestamp(self):
+        Timestamp(self.ts)
+
 
 class TimestampProperties:
     _tzs = [None, pytz.timezone("Europe/Amsterdam"), pytz.UTC, dateutil.tz.tzutc()]
diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index d0cf92b60fe0d..a0e1c964dd365 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -109,7 +109,9 @@ Deprecations
 
 Performance improvements
 ~~~~~~~~~~~~~~~~~~~~~~~~
+
 - Performance improvement in :class:`Timedelta` constructor (:issue:`30543`)
+- Performance improvement in :class:`Timestamp` constructor (:issue:`30543`)
 -
 -
 
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 36566b55e74ad..4915671aa6512 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -391,7 +391,18 @@ class Timestamp(_Timestamp):
             # User passed tzinfo instead of tz; avoid silently ignoring
             tz, tzinfo = tzinfo, None
 
-        if isinstance(ts_input, str):
+        # GH 30543 if pd.Timestamp already passed, return it
+        # check that only ts_input is passed
+        # checking verbosely, because cython doesn't optimize
+        # list comprehensions (as of cython 0.29.x)
+        if (isinstance(ts_input, Timestamp) and freq is None and
+                tz is None and unit is None and year is None and
+                month is None and day is None and hour is None and
+                minute is None and second is None and
+                microsecond is None and nanosecond is None and
+                tzinfo is None):
+            return ts_input
+        elif isinstance(ts_input, str):
             # User passed a date string to parse.
             # Check that the user didn't also pass a date attribute kwarg.
             if any(arg is not None for arg in _date_attributes):
diff --git a/pandas/tests/indexes/datetimes/test_constructors.py b/pandas/tests/indexes/datetimes/test_constructors.py
index b6013c3939793..68285d41bda70 100644
--- a/pandas/tests/indexes/datetimes/test_constructors.py
+++ b/pandas/tests/indexes/datetimes/test_constructors.py
@@ -957,3 +957,10 @@ def test_timedelta_constructor_identity():
     expected = pd.Timedelta(np.timedelta64(1, "s"))
     result = pd.Timedelta(expected)
     assert result is expected
+
+
+def test_timestamp_constructor_identity():
+    # Test for #30543
+    expected = pd.Timestamp("2017-01-01T12")
+    result = pd.Timestamp(expected)
+    assert result is expected
diff --git a/pandas/tests/indexes/datetimes/test_timezones.py b/pandas/tests/indexes/datetimes/test_timezones.py
index c785eb67e5184..cd8e8c3542cce 100644
--- a/pandas/tests/indexes/datetimes/test_timezones.py
+++ b/pandas/tests/indexes/datetimes/test_timezones.py
@@ -2,7 +2,6 @@
 Tests for DatetimeIndex timezone-related methods
 """
 from datetime import date, datetime, time, timedelta, tzinfo
-from distutils.version import LooseVersion
 
 import dateutil
 from dateutil.tz import gettz, tzlocal
@@ -11,7 +10,6 @@
 import pytz
 
 from pandas._libs.tslibs import conversion, timezones
-from pandas.compat._optional import _get_version
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -583,15 +581,7 @@ def test_dti_construction_ambiguous_endpoint(self, tz):
             ["US/Pacific", "shift_forward", "2019-03-10 03:00"],
             ["dateutil/US/Pacific", "shift_forward", "2019-03-10 03:00"],
             ["US/Pacific", "shift_backward", "2019-03-10 01:00"],
-            pytest.param(
-                "dateutil/US/Pacific",
-                "shift_backward",
-                "2019-03-10 01:00",
-                marks=pytest.mark.xfail(
-                    LooseVersion(_get_version(dateutil)) < LooseVersion("2.7.0"),
-                    reason="GH 31043",
-                ),
-            ),
+            ["dateutil/US/Pacific", "shift_backward", "2019-03-10 01:00"],
             ["US/Pacific", timedelta(hours=1), "2019-03-10 03:00"],
         ],
     )