diff --git a/sdk/core/azure-core/azure/core/_pipeline_client.py b/sdk/core/azure-core/azure/core/_pipeline_client.py
index ec32e2b20964..44e5995c5f84 100644
--- a/sdk/core/azure-core/azure/core/_pipeline_client.py
+++ b/sdk/core/azure-core/azure/core/_pipeline_client.py
@@ -39,7 +39,6 @@
     RequestIdPolicy,
     RetryPolicy,
 )
-from .pipeline.transport import RequestsTransport
 from .pipeline._tools import to_rest_response as _to_rest_response
 
 try:
@@ -181,6 +180,7 @@ def _build_pipeline(self, config, **kwargs): # pylint: disable=no-self-use
                 policies = policies_1
 
         if not transport:
+            from .pipeline.transport import RequestsTransport
             transport = RequestsTransport(**kwargs)
 
         return Pipeline(transport, policies)
diff --git a/sdk/core/azure-core/azure/core/pipeline/policies/_utils.py b/sdk/core/azure-core/azure/core/pipeline/policies/_utils.py
index 326b2099bc11..6712178a61b5 100644
--- a/sdk/core/azure-core/azure/core/pipeline/policies/_utils.py
+++ b/sdk/core/azure-core/azure/core/pipeline/policies/_utils.py
@@ -25,8 +25,7 @@
 # --------------------------------------------------------------------------
 import datetime
 import email.utils
-from requests.structures import CaseInsensitiveDict
-from ...utils._utils import _FixedOffset
+from ...utils._utils import _FixedOffset, _case_insensitive_dict
 
 def _parse_http_date(text):
     """Parse a HTTP date format into datetime."""
@@ -58,7 +57,7 @@ def get_retry_after(response):
     :return: Value of Retry-After in seconds.
     :rtype: float or None
     """
-    headers = CaseInsensitiveDict(response.http_response.headers)
+    headers = _case_insensitive_dict(response.http_response.headers)
     retry_after = headers.get("retry-after")
     if retry_after:
         return parse_retry_after(retry_after)
diff --git a/sdk/core/azure-core/azure/core/pipeline/transport/__init__.py b/sdk/core/azure-core/azure/core/pipeline/transport/__init__.py
index a177dcbc8443..57067c36bcbd 100644
--- a/sdk/core/azure-core/azure/core/pipeline/transport/__init__.py
+++ b/sdk/core/azure-core/azure/core/pipeline/transport/__init__.py
@@ -26,82 +26,133 @@
 
 import sys
 from ._base import HttpTransport, HttpRequest, HttpResponse
-from ._requests_basic import RequestsTransport, RequestsTransportResponse
 
 __all__ = [
     'HttpTransport',
     'HttpRequest',
     'HttpResponse',
-    'RequestsTransport',
-    'RequestsTransportResponse',
 ]
 
 # pylint: disable=unused-import, redefined-outer-name
 try:
-    from ._base_async import AsyncHttpTransport, AsyncHttpResponse
-    from ._requests_asyncio import AsyncioRequestsTransport, AsyncioRequestsTransportResponse
+    from ._requests_basic import RequestsTransport, RequestsTransportResponse
     __all__.extend([
-        'AsyncHttpTransport',
-        'AsyncHttpResponse',
-        'AsyncioRequestsTransport',
-        'AsyncioRequestsTransportResponse'
+        'RequestsTransport',
+        'RequestsTransportResponse',
     ])
+    try:
+        from ._base_async import AsyncHttpTransport, AsyncHttpResponse
+        from ._requests_asyncio import AsyncioRequestsTransport, AsyncioRequestsTransportResponse
 
-    if sys.version_info >= (3, 7):
         __all__.extend([
-            'TrioRequestsTransport',
-            'TrioRequestsTransportResponse',
-            'AioHttpTransport',
-            'AioHttpTransportResponse',
+            'AsyncHttpTransport',
+            'AsyncHttpResponse',
+            'AsyncioRequestsTransport',
+            'AsyncioRequestsTransportResponse'
         ])
 
-        def __dir__():
-            return __all__
-
-        def __getattr__(name):
-            if name == 'AioHttpTransport':
-                try:
-                    from ._aiohttp import AioHttpTransport
-                    return AioHttpTransport
-                except ImportError:
-                    raise ImportError("aiohttp package is not installed")
-            if name == 'AioHttpTransportResponse':
-                try:
-                    from ._aiohttp import AioHttpTransportResponse
-                    return AioHttpTransportResponse
-                except ImportError:
-                    raise ImportError("aiohttp package is not installed")
-            if name == 'TrioRequestsTransport':
-                try:
-                    from ._requests_trio import TrioRequestsTransport
-                    return TrioRequestsTransport
-                except ImportError:
-                    raise ImportError("trio package is not installed")
-            if name == 'TrioRequestsTransportResponse':
-                try:
-                    from ._requests_trio import TrioRequestsTransportResponse
-                    return TrioRequestsTransportResponse
-                except ImportError:
-                    raise ImportError("trio package is not installed")
-            return name
-
-    else:
-        try:
-            from ._requests_trio import TrioRequestsTransport, TrioRequestsTransportResponse
+        if sys.version_info >= (3, 7):
             __all__.extend([
                 'TrioRequestsTransport',
-                'TrioRequestsTransportResponse'
+                'TrioRequestsTransportResponse',
+                'AioHttpTransport',
+                'AioHttpTransportResponse',
             ])
-        except ImportError:
-            pass  # Trio not installed
 
-        try:
-            from ._aiohttp import AioHttpTransport, AioHttpTransportResponse
+            def __dir__():
+                return __all__
+
+            def __getattr__(name):
+                if name == 'AioHttpTransport':
+                    try:
+                        from ._aiohttp import AioHttpTransport
+                        return AioHttpTransport
+                    except ImportError:
+                        raise ImportError("aiohttp package is not installed")
+                if name == 'AioHttpTransportResponse':
+                    try:
+                        from ._aiohttp import AioHttpTransportResponse
+                        return AioHttpTransportResponse
+                    except ImportError:
+                        raise ImportError("aiohttp package is not installed")
+                if name == 'TrioRequestsTransport':
+                    try:
+                        from ._requests_trio import TrioRequestsTransport
+                        return TrioRequestsTransport
+                    except ImportError:
+                        raise ImportError("trio package is not installed")
+                if name == 'TrioRequestsTransportResponse':
+                    try:
+                        from ._requests_trio import TrioRequestsTransportResponse
+                        return TrioRequestsTransportResponse
+                    except ImportError:
+                        raise ImportError("trio package is not installed")
+                return name
+
+        else:
+            try:
+                from ._requests_trio import TrioRequestsTransport, TrioRequestsTransportResponse
+
+                __all__.extend([
+                    'TrioRequestsTransport',
+                    'TrioRequestsTransportResponse'
+                ])
+            except ImportError:
+                pass  # Trio not installed
+
+            try:
+                from ._aiohttp import AioHttpTransport, AioHttpTransportResponse
+
+                __all__.extend([
+                    'AioHttpTransport',
+                    'AioHttpTransportResponse',
+                ])
+            except ImportError:
+                pass  # Aiohttp not installed
+    except (ImportError, SyntaxError):
+        # requests library is installed but asynchronous pipelines not supported.
+        pass
+except (ImportError, SyntaxError):
+    # requests library is not installed
+    try:
+        from ._base_async import AsyncHttpTransport, AsyncHttpResponse
+        __all__.extend([
+            'AsyncHttpTransport',
+            'AsyncHttpResponse',
+        ])
+
+        if sys.version_info >= (3, 7):
             __all__.extend([
                 'AioHttpTransport',
                 'AioHttpTransportResponse',
             ])
-        except ImportError:
-            pass  # Aiohttp not installed
-except (ImportError, SyntaxError):
-    pass  # Asynchronous pipelines not supported.
+
+            def __dir__():
+                return __all__
+
+            def __getattr__(name):
+                if name == 'AioHttpTransport':
+                    try:
+                        from ._aiohttp import AioHttpTransport
+                        return AioHttpTransport
+                    except ImportError:
+                        raise ImportError("aiohttp package is not installed")
+                if name == 'AioHttpTransportResponse':
+                    try:
+                        from ._aiohttp import AioHttpTransportResponse
+                        return AioHttpTransportResponse
+                    except ImportError:
+                        raise ImportError("aiohttp package is not installed")
+                return name
+
+        else:
+            try:
+                from ._aiohttp import AioHttpTransport, AioHttpTransportResponse
+                __all__.extend([
+                    'AioHttpTransport',
+                    'AioHttpTransportResponse',
+                ])
+            except ImportError:
+                pass  # Aiohttp not installed
+    except (ImportError, SyntaxError):
+        pass  # Asynchronous pipelines not supported.
diff --git a/sdk/core/azure-core/azure/core/utils/_utils.py b/sdk/core/azure-core/azure/core/utils/_utils.py
index 5f3133e02955..08ae1ea21da7 100644
--- a/sdk/core/azure-core/azure/core/utils/_utils.py
+++ b/sdk/core/azure-core/azure/core/utils/_utils.py
@@ -99,6 +99,8 @@ def _case_insensitive_dict(*args, **kwargs):
         # multidict is installed by aiohttp
         from multidict import CIMultiDict
 
+        if len(kwargs) == 0 and len(args) == 1 and (not args[0]):
+            return CIMultiDict()    # in case of case_insensitive_dict(None), we don't want to raise exception
         return CIMultiDict(*args, **kwargs)
     except ImportError:
         raise ValueError(