diff --git a/tests/IronPython.Tests/Cases/CPythonCasesManifest.ini b/tests/IronPython.Tests/Cases/CPythonCasesManifest.ini
index d355219b6..480ee70b6 100644
--- a/tests/IronPython.Tests/Cases/CPythonCasesManifest.ini
+++ b/tests/IronPython.Tests/Cases/CPythonCasesManifest.ini
@@ -603,9 +603,8 @@ Ignore=true
 [CPython.test_lib2to3]
 Ignore=true
 
-# TODO: 3.6
-#[CPython.test_linecache]
-#Ignore=true # blocked by https://github.com/IronLanguages/ironpython3/issues/1245 - using the test_linecache_stdlib approach makes the issue disappear...
+[CPython.test_linecache] # IronPython.test_linecache_stdlib
+Ignore=true
 
 [CPython.test_list]
 IsolationLevel=ENGINE
diff --git a/tests/suite/test_datetime_stdlib.py b/tests/suite/test_datetime_stdlib.py
index 831a69d69..54742c183 100644
--- a/tests/suite/test_datetime_stdlib.py
+++ b/tests/suite/test_datetime_stdlib.py
@@ -63,12 +63,10 @@ def load_tests(loader, standard_tests, pattern):
                 test.datetimetester.TestDateTime('test_compat_unpickle'), # TypeError: function takes at least 3 arguments (1 given)
                 test.datetimetester.TestDateTime('test_isoformat'), # TypeError: isoformat() got an unexpected keyword argument 'timespec'
                 test.datetimetester.TestDateTime('test_subclass_replace'), # TypeError: replace() got an unexpected keyword argument 'year'
-                test.datetimetester.TestDateTime('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
                 test.datetimetester.TestDateTimeTZ('test_bad_constructor_arguments'), # https://github.com/IronLanguages/ironpython3/issues/1459
                 test.datetimetester.TestDateTimeTZ('test_compat_unpickle'), # TypeError: function takes at least 3 arguments (2 given)
                 test.datetimetester.TestDateTimeTZ('test_isoformat'), # TypeError: isoformat() got an unexpected keyword argument 'timespec'
                 test.datetimetester.TestDateTimeTZ('test_subclass_replace'), # TypeError: replace() got an unexpected keyword argument 'year'
-                test.datetimetester.TestDateTimeTZ('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
                 test.datetimetester.TestLocalTimeDisambiguation('test_comparison'), # https://github.com/IronLanguages/ironpython3/issues/1459
                 test.datetimetester.TestLocalTimeDisambiguation('test_constructors'), # https://github.com/IronLanguages/ironpython3/issues/1459
                 test.datetimetester.TestLocalTimeDisambiguation('test_dst'), # https://github.com/IronLanguages/ironpython3/issues/1459
@@ -91,7 +89,6 @@ def load_tests(loader, standard_tests, pattern):
                 test.datetimetester.TestSubclassDateTime('test_compat_unpickle'), # TypeError: function takes at least 3 arguments (1 given)
                 test.datetimetester.TestSubclassDateTime('test_isoformat'), # TypeError: isoformat() got an unexpected keyword argument 'timespec'
                 test.datetimetester.TestSubclassDateTime('test_subclass_replace'), # TypeError: replace() got an unexpected keyword argument 'year'
-                test.datetimetester.TestSubclassDateTime('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
                 test.datetimetester.TestTime('test_backdoor_resistance'), # AssertionError: "^bad tzinfo state arg$" does not match "expected Int32, got bytes"
                 test.datetimetester.TestTime('test_compat_unpickle'), # TypeError: expected Int32, got str
                 test.datetimetester.TestTime('test_isoformat'), # TypeError: isoformat() takes no arguments (1 given)
@@ -112,6 +109,12 @@ def load_tests(loader, standard_tests, pattern):
                 test.datetimetester.TestTimeDelta('test_overflow'), # rounding differences
             ]
         if sys.version_info >= (3, 6):
+            skip_tests += [
+                # these can fail with a ValueError if the current time zone is not UTC
+                test.datetimetester.TestDateTime('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
+                test.datetimetester.TestDateTimeTZ('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
+                test.datetimetester.TestSubclassDateTime('test_timestamp_limits'), # ValueError: The added or subtracted value results in an un-representable DateTime.
+            ]
             for test_or_suite in tests:
                 if isinstance(test_or_suite, test.datetimetester.ZoneInfoCompleteTest):
                     for t in test_or_suite:
diff --git a/tests/suite/test_linecache_stdlib.py b/tests/suite/test_linecache_stdlib.py
new file mode 100644
index 000000000..162deb834
--- /dev/null
+++ b/tests/suite/test_linecache_stdlib.py
@@ -0,0 +1,31 @@
+# Licensed to the .NET Foundation under one or more agreements.
+# The .NET Foundation licenses this file to you under the Apache 2.0 License.
+# See the LICENSE file in the project root for more information.
+
+##
+## Run selected tests from test_linecache from StdLib
+##
+
+import sys
+
+from iptest import is_ironpython, generate_suite, run_test
+
+import test.test_linecache
+
+def load_tests(loader, standard_tests, pattern):
+    tests = loader.loadTestsFromModule(test.test_linecache, pattern=pattern)
+
+    if is_ironpython:
+        # There are no failing tests when running via test_linecache_stdlib, but when running test_linecache directly there are some failures.
+        # See https://github.com/IronLanguages/ironpython3/issues/1245 for details.
+
+        failing_tests = []
+
+        skip_tests = []
+
+        return generate_suite(tests, failing_tests, skip_tests)
+
+    else:
+        return tests
+
+run_test(__name__)
diff --git a/tests/suite/test_typing_stdlib.py b/tests/suite/test_typing_stdlib.py
index 890d6a63f..b072f256c 100644
--- a/tests/suite/test_typing_stdlib.py
+++ b/tests/suite/test_typing_stdlib.py
@@ -8,7 +8,7 @@
 
 import sys
 
-from iptest import is_ironpython, generate_suite, run_test
+from iptest import is_ironpython, generate_suite, run_test, is_netcoreapp
 
 import test.test_typing
 
@@ -49,6 +49,10 @@ def load_tests(loader, standard_tests, pattern):
                 test.test_typing.NamedTupleTests('test_annotation_usage_with_default'), # TypeError: __new__() takes exactly 1 argument (2 given)
                 test.test_typing.NamedTupleTests('test_annotation_usage_with_methods'), # TypeError: __new__() takes exactly 1 argument (2 given)
             ]
+            if is_netcoreapp:
+                failing_tests += [
+                    test.test_typing.CollectionsAbcTests('test_awaitable'), # https://github.com/IronLanguages/ironpython3/issues/2054
+                ]
 
         skip_tests = []
         if sys.version_info >= (3, 6):