diff --git a/sdk/core/Azure.Core/api/Azure.Core.net461.cs b/sdk/core/Azure.Core/api/Azure.Core.net461.cs
index 4a36fc58ad10..d5df397dda3d 100644
--- a/sdk/core/Azure.Core/api/Azure.Core.net461.cs
+++ b/sdk/core/Azure.Core/api/Azure.Core.net461.cs
@@ -488,7 +488,7 @@ public HttpMessage(Azure.Core.Request request, Azure.Core.ResponseClassifier res
         public Azure.Core.MessageProcessingContext ProcessingContext { get { throw null; } }
         public new Azure.Core.Request Request { get { throw null; } }
         public new Azure.Response Response { get { throw null; } set { } }
-        public Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
+        public new Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
         public System.IO.Stream? ExtractResponseContent() { throw null; }
         public void SetProperty(string name, object value) { }
         public bool TryGetProperty(string name, out object? value) { throw null; }
diff --git a/sdk/core/Azure.Core/api/Azure.Core.net472.cs b/sdk/core/Azure.Core/api/Azure.Core.net472.cs
index 4a36fc58ad10..d5df397dda3d 100644
--- a/sdk/core/Azure.Core/api/Azure.Core.net472.cs
+++ b/sdk/core/Azure.Core/api/Azure.Core.net472.cs
@@ -488,7 +488,7 @@ public HttpMessage(Azure.Core.Request request, Azure.Core.ResponseClassifier res
         public Azure.Core.MessageProcessingContext ProcessingContext { get { throw null; } }
         public new Azure.Core.Request Request { get { throw null; } }
         public new Azure.Response Response { get { throw null; } set { } }
-        public Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
+        public new Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
         public System.IO.Stream? ExtractResponseContent() { throw null; }
         public void SetProperty(string name, object value) { }
         public bool TryGetProperty(string name, out object? value) { throw null; }
diff --git a/sdk/core/Azure.Core/api/Azure.Core.net6.0.cs b/sdk/core/Azure.Core/api/Azure.Core.net6.0.cs
index b1d3e8dac712..b5a657f013dc 100644
--- a/sdk/core/Azure.Core/api/Azure.Core.net6.0.cs
+++ b/sdk/core/Azure.Core/api/Azure.Core.net6.0.cs
@@ -488,7 +488,7 @@ public HttpMessage(Azure.Core.Request request, Azure.Core.ResponseClassifier res
         public Azure.Core.MessageProcessingContext ProcessingContext { get { throw null; } }
         public new Azure.Core.Request Request { get { throw null; } }
         public new Azure.Response Response { get { throw null; } set { } }
-        public Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
+        public new Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
         public System.IO.Stream? ExtractResponseContent() { throw null; }
         public void SetProperty(string name, object value) { }
         public bool TryGetProperty(string name, out object? value) { throw null; }
diff --git a/sdk/core/Azure.Core/api/Azure.Core.netstandard2.0.cs b/sdk/core/Azure.Core/api/Azure.Core.netstandard2.0.cs
index 4a36fc58ad10..d5df397dda3d 100644
--- a/sdk/core/Azure.Core/api/Azure.Core.netstandard2.0.cs
+++ b/sdk/core/Azure.Core/api/Azure.Core.netstandard2.0.cs
@@ -488,7 +488,7 @@ public HttpMessage(Azure.Core.Request request, Azure.Core.ResponseClassifier res
         public Azure.Core.MessageProcessingContext ProcessingContext { get { throw null; } }
         public new Azure.Core.Request Request { get { throw null; } }
         public new Azure.Response Response { get { throw null; } set { } }
-        public Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
+        public new Azure.Core.ResponseClassifier ResponseClassifier { get { throw null; } set { } }
         public System.IO.Stream? ExtractResponseContent() { throw null; }
         public void SetProperty(string name, object value) { }
         public bool TryGetProperty(string name, out object? value) { throw null; }
diff --git a/sdk/core/Azure.Core/src/HttpMessage.cs b/sdk/core/Azure.Core/src/HttpMessage.cs
index 58243be82dab..467b5dafa317 100644
--- a/sdk/core/Azure.Core/src/HttpMessage.cs
+++ b/sdk/core/Azure.Core/src/HttpMessage.cs
@@ -63,19 +63,10 @@ public HttpMessage(Request request, ResponseClassifier responseClassifier)
         /// <summary>
         /// The <see cref="ResponseClassifier"/> instance to use for response classification during pipeline invocation.
         /// </summary>
-        public ResponseClassifier ResponseClassifier
+        public new ResponseClassifier ResponseClassifier
         {
-            get
-            {
-                if (MessageClassifier is not ResponseClassifier classifier)
-                {
-                    throw new InvalidOperationException($"Invalid ResponseClassifier set on message: '{base.MessageClassifier}'.");
-                }
-
-                return classifier;
-            }
-
-            set => MessageClassifier = value;
+            get => (ResponseClassifier)base.ResponseClassifier;
+            set => base.ResponseClassifier = value;
         }
 
         internal int RetryNumber { get; set; }
diff --git a/sdk/core/Azure.Core/src/Pipeline/RetryPolicy.AzurePolicy.cs b/sdk/core/Azure.Core/src/Pipeline/RetryPolicy.AzurePolicy.cs
index 69a83981636c..06b6a1ea95c5 100644
--- a/sdk/core/Azure.Core/src/Pipeline/RetryPolicy.AzurePolicy.cs
+++ b/sdk/core/Azure.Core/src/Pipeline/RetryPolicy.AzurePolicy.cs
@@ -58,10 +58,10 @@ protected override async ValueTask OnRequestSentAsync(PipelineMessage message)
             _elapsedTime = (_afterProcess - _beforeProcess) / (double)Stopwatch.Frequency;
         }
 
-        protected override bool ShouldRetryCore(PipelineMessage message, Exception? exception)
+        protected override bool ShouldRetry(PipelineMessage message, Exception? exception)
             => _pipelinePolicy.ShouldRetry(AssertHttpMessage(message), exception);
 
-        protected override async ValueTask<bool> ShouldRetryCoreAsync(PipelineMessage message, Exception? exception)
+        protected override async ValueTask<bool> ShouldRetryAsync(PipelineMessage message, Exception? exception)
             => await _pipelinePolicy.ShouldRetryAsync(AssertHttpMessage(message), exception).ConfigureAwait(false);
 
         protected override void OnTryComplete(PipelineMessage message)
@@ -77,7 +77,7 @@ protected override void OnTryComplete(PipelineMessage message)
             _elapsedTime = default;
         }
 
-        protected override TimeSpan GetNextDelayCore(PipelineMessage message, int tryCount)
+        protected override TimeSpan GetNextDelay(PipelineMessage message, int tryCount)
         {
             HttpMessage httpMessage = AssertHttpMessage(message);
 
@@ -87,10 +87,10 @@ protected override TimeSpan GetNextDelayCore(PipelineMessage message, int tryCou
             return _delayStrategy.GetNextDelay(response, tryCount + 1);
         }
 
-        protected override async Task WaitCoreAsync(TimeSpan time, CancellationToken cancellationToken)
+        protected override async Task WaitAsync(TimeSpan time, CancellationToken cancellationToken)
             => await _pipelinePolicy.WaitAsync(time, cancellationToken).ConfigureAwait(false);
 
-        protected override void WaitCore(TimeSpan time, CancellationToken cancellationToken)
+        protected override void Wait(TimeSpan time, CancellationToken cancellationToken)
             => _pipelinePolicy.Wait(time, cancellationToken);
 
         private static HttpMessage AssertHttpMessage(PipelineMessage message)
diff --git a/sdk/core/Azure.Core/tests/common/TestClients/MapsClient/MapsClient.cs b/sdk/core/Azure.Core/tests/common/TestClients/MapsClient/MapsClient.cs
index 7c3e88a230f1..493d6f113516 100644
--- a/sdk/core/Azure.Core/tests/common/TestClients/MapsClient/MapsClient.cs
+++ b/sdk/core/Azure.Core/tests/common/TestClients/MapsClient/MapsClient.cs
@@ -71,7 +71,7 @@ private HttpMessage CreateGetLocationRequest(string ipAddress, RequestContext co
     {
         HttpMessage message = _pipeline.CreateMessage();
         message.Apply(context);
-        message.MessageClassifier = PipelineMessageClassifier.Create(stackalloc ushort[] { 200 });
+        message.ResponseClassifier = new StatusCodeClassifier(stackalloc ushort[] { 200 });
 
         Request request = message.Request;
         request.Method = RequestMethod.Get;
diff --git a/sdk/core/System.ClientModel/tests/client/MapsClient/MapsClient.cs b/sdk/core/System.ClientModel/tests/client/MapsClient/MapsClient.cs
index c719650de6b6..a4c18222a771 100644
--- a/sdk/core/System.ClientModel/tests/client/MapsClient/MapsClient.cs
+++ b/sdk/core/System.ClientModel/tests/client/MapsClient/MapsClient.cs
@@ -69,7 +69,7 @@ public virtual ClientResult GetCountryCode(string ipAddress, RequestOptions opti
     private PipelineMessage CreateGetLocationRequest(string ipAddress, RequestOptions options)
     {
         PipelineMessage message = _pipeline.CreateMessage();
-        message.MessageClassifier = PipelineMessageClassifier.Create(stackalloc ushort[] { 200 });
+        message.ResponseClassifier = PipelineMessageClassifier.Create(stackalloc ushort[] { 200 });
 
         PipelineRequest request = message.Request;
         request.Method = "GET";
diff --git a/sdk/core/System.ClientModel/tests/client/OpenAIClient/OpenAIClient.cs b/sdk/core/System.ClientModel/tests/client/OpenAIClient/OpenAIClient.cs
index c6dee54e8df1..14601dae3fd1 100644
--- a/sdk/core/System.ClientModel/tests/client/OpenAIClient/OpenAIClient.cs
+++ b/sdk/core/System.ClientModel/tests/client/OpenAIClient/OpenAIClient.cs
@@ -71,7 +71,7 @@ public virtual ClientResult GetCompletions(string deploymentId, BinaryContent co
     internal PipelineMessage CreateGetCompletionsRequest(string deploymentId, BinaryContent content, RequestOptions options)
     {
         PipelineMessage message = _pipeline.CreateMessage();
-        message.MessageClassifier = MessageClassifier200;
+        message.ResponseClassifier = MessageClassifier200;
 
         PipelineRequest request = message.Request;
         request.Method = "POST";
diff --git a/sdk/core/System.ClientModel/tests/nullableenabledclient/MapsClient/MapsClient.cs b/sdk/core/System.ClientModel/tests/nullableenabledclient/MapsClient/MapsClient.cs
index 8b7b2ee0a709..aaa2d23a75d8 100644
--- a/sdk/core/System.ClientModel/tests/nullableenabledclient/MapsClient/MapsClient.cs
+++ b/sdk/core/System.ClientModel/tests/nullableenabledclient/MapsClient/MapsClient.cs
@@ -88,7 +88,7 @@ public virtual ClientResult GetCountryCode(string ipAddress, RequestOptions? opt
     private PipelineMessage CreateGetLocationRequest(string ipAddress, RequestOptions options)
     {
         PipelineMessage message = _pipeline.CreateMessage();
-        message.MessageClassifier = PipelineMessageClassifier.Create(stackalloc ushort[] { 200 });
+        message.ResponseClassifier = PipelineMessageClassifier.Create(stackalloc ushort[] { 200 });
 
         PipelineRequest request = message.Request;
         request.Method = "GET";