diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_2681_handler_type_naming_binds_all_exchanges.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_2681_handler_type_naming_binds_all_exchanges.cs
index c89f2becb..4f50fc63f 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_2681_handler_type_naming_binds_all_exchanges.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_2681_handler_type_naming_binds_all_exchanges.cs
@@ -46,7 +46,13 @@ public async ValueTask InitializeAsync()
         _runtime = _host.Services.GetRequiredService<IWolverineRuntime>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_host != null) await _host.StopAsync();
+    }
 
     [Fact]
     public void handler_queue_is_bound_to_every_handled_message_exchange()
@@ -127,7 +133,13 @@ public async ValueTask InitializeAsync()
         _runtime = _host.Services.GetRequiredService<IWolverineRuntime>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_host != null) await _host.StopAsync();
+    }
 
     [Fact]
     public void user_custom_binding_is_not_double_added_by_the_convention()
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_3041_saga_and_handler_with_handler_type_naming.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_3041_saga_and_handler_with_handler_type_naming.cs
index 8a18ecd02..6e5fa0ee0 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_3041_saga_and_handler_with_handler_type_naming.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/Bug_3041_saga_and_handler_with_handler_type_naming.cs
@@ -39,7 +39,13 @@ public async ValueTask InitializeAsync()
         _runtime = _host.Services.GetRequiredService<IWolverineRuntime>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_host != null) await _host.StopAsync();
+    }
 
     [Fact]
     public void both_the_saga_and_the_regular_handler_get_listener_queues()
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/ConventionalRoutingContext.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/ConventionalRoutingContext.cs
index b17ba0ebf..d9c303d10 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/ConventionalRoutingContext.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/ConventionalRoutingContext.cs
@@ -14,7 +14,16 @@ public static class ConventionalRoutingTestDefaults
 }
 
 
-public abstract class ConventionalRoutingContext : IDisposable
+/// <summary>
+///     GH-3965. Note the async disposal. Every conventionally routed <see cref="ConventionallyRoutedMessage" />
+///     lands on one FIXED queue -- the type carries <c>[MessageIdentity("routed")]</c>, so the queue is
+///     literally <c>routed</c> -- and several classes in this namespace stand up listeners on it.
+///     <see cref="IHost.Dispose" /> does NOT run <c>IHostedService.StopAsync</c>, so disposing synchronously
+///     left those consumers attached to the broker after the test finished, and a later test's message was
+///     delivered to a leaked consumer belonging to an already-completed class. That shows up as a tracked
+///     session containing <c>Sent</c> and no <c>Received</c> at all.
+/// </summary>
+public abstract class ConventionalRoutingContext : IDisposable, IAsyncDisposable
 {
     private IHost _host = null!;
 
@@ -55,6 +64,22 @@ public void Dispose()
         _host?.Dispose();
     }
 
+    public ValueTask DisposeAsync() => DisposeHostAsync();
+
+    /// <summary>
+    ///     Stops the host so its Rabbit consumers are actually cancelled, then disposes it. Derived classes
+    ///     that implement <c>IAsyncLifetime</c> shadow the interface implementation above, so they must call
+    ///     this from their own <c>DisposeAsync</c> rather than returning a completed ValueTask.
+    /// </summary>
+    protected async ValueTask DisposeHostAsync()
+    {
+        if (_host == null) return;
+
+        await _host.StopAsync();
+        _host.Dispose();
+        _host = null!;
+    }
+
     internal async Task ConfigureConventions(Action<RabbitMqMessageRoutingConvention> configure)
     {
         _host = await WolverineHost.ForAsync(opts =>
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing.cs
index 4a79971d0..60a7d9613 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing.cs
@@ -27,7 +27,14 @@ public async ValueTask InitializeAsync()
         });
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_sender != null) await _sender.StopAsync();
+        if (_receiver != null) await _receiver.StopAsync();
+    }
 
     public void Dispose()
     {
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_custom_exchange.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_custom_exchange.cs
index fc5fd048d..97f6c6e68 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_custom_exchange.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_custom_exchange.cs
@@ -57,7 +57,14 @@ public async ValueTask InitializeAsync()
 
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_sender != null) await _sender.StopAsync();
+        if (_receiver != null) await _receiver.StopAsync();
+    }
 
     public void Dispose()
     {
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_with_prefix.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_with_prefix.cs
index fc6d5656d..90b56258c 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_with_prefix.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/end_to_end_with_conventional_routing_with_prefix.cs
@@ -38,7 +38,14 @@ public async ValueTask InitializeAsync()
         });
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_sender != null) await _sender.StopAsync();
+        if (_receiver != null) await _receiver.StopAsync();
+    }
 
     public void Dispose()
     {
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_all_defaults.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_all_defaults.cs
index d9436c9bd..cb485a958 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_all_defaults.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_all_defaults.cs
@@ -17,7 +17,8 @@ public async ValueTask InitializeAsync()
         theEndpoint = (await theRuntime()).Endpoints.EndpointFor(theExpectedUri).ShouldBeOfType<RabbitMqQueue>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: shadows ConventionalRoutingContext.DisposeAsync -- must stop the host itself.
+    ValueTask IAsyncDisposable.DisposeAsync() => DisposeHostAsync();
 
     [Fact]
     public void endpoint_should_be_a_listener()
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_overridden_queue_naming.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_overridden_queue_naming.cs
index 57f84ce69..788db92e3 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_overridden_queue_naming.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_listening_endpoint_with_overridden_queue_naming.cs
@@ -22,7 +22,8 @@ await ConfigureConventions(c =>
         theEndpoint = (await theRuntime()).Endpoints.EndpointFor(theExpectedUri).ShouldBeOfType<RabbitMqQueue>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: shadows ConventionalRoutingContext.DisposeAsync -- must stop the host itself.
+    ValueTask IAsyncDisposable.DisposeAsync() => DisposeHostAsync();
 
     [Fact]
     public void endpoint_should_be_a_listener()
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_sender_with_all_defaults.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_sender_with_all_defaults.cs
index 83eededbd..2f47be2ae 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_sender_with_all_defaults.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_discovering_a_sender_with_all_defaults.cs
@@ -20,7 +20,8 @@ public async ValueTask InitializeAsync()
         theRoute = ((await PublishingRoutesFor<ConventionallyRoutedMessage>()).Single() as MessageRoute)!;
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: shadows ConventionalRoutingContext.DisposeAsync -- must stop the host itself.
+    ValueTask IAsyncDisposable.DisposeAsync() => DisposeHostAsync();
 
     [Fact]
     public void should_have_exactly_one_route()
diff --git a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_using_handler_type_naming.cs b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_using_handler_type_naming.cs
index 7ef068883..00c75afd0 100644
--- a/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_using_handler_type_naming.cs
+++ b/src/Transports/RabbitMQ/Wolverine.RabbitMQ.Tests/ConventionalRouting/when_using_handler_type_naming.cs
@@ -31,7 +31,13 @@ public async ValueTask InitializeAsync()
         _runtime = _host.Services.GetRequiredService<IWolverineRuntime>();
     }
 
-    ValueTask IAsyncDisposable.DisposeAsync() => ValueTask.CompletedTask;
+    // GH-3965: IHost.Dispose() does not run StopAsync, so a synchronous teardown left this
+    // class's Rabbit consumers attached to a SHARED, fixed queue name and stealing later
+    // tests' messages. Stop the hosts for real.
+    async ValueTask IAsyncDisposable.DisposeAsync()
+    {
+        if (_host != null) await _host.StopAsync();
+    }
 
     [Fact]
     public void listener_endpoint_should_be_named_after_handler_type()