diff --git a/src/Transport/Receiving/MessagePump.cs b/src/Transport/Receiving/MessagePump.cs
index c8ba86ef..b5c98efd 100644
--- a/src/Transport/Receiving/MessagePump.cs
+++ b/src/Transport/Receiving/MessagePump.cs
@@ -243,6 +243,10 @@ async Task ProcessMessage(Task<Message> receiveTask)
                         await receiver.SafeAbandonAsync(pushSettings.RequiredTransactionMode, lockToken).ConfigureAwait(false);
                     }
                 }
+                catch (Exception onErrorException) when (onErrorException is MessageLockLostException || onErrorException is ServiceBusTimeoutException)
+                {
+                    logger.Debug("Failed to execute recoverability.", onErrorException);
+                }
                 catch (Exception onErrorException)
                 {
                     criticalError.Raise($"Failed to execute recoverability policy for message with native ID: `{message.MessageId}`", onErrorException);
diff --git a/src/TransportTests/When_MessageLockLostException_is_thrown.cs b/src/TransportTests/When_MessageLockLostException_is_thrown.cs
new file mode 100644
index 00000000..c8e4596e
--- /dev/null
+++ b/src/TransportTests/When_MessageLockLostException_is_thrown.cs
@@ -0,0 +1,54 @@
+namespace NServiceBus.Transport.AzureServiceBus.TransportTests
+{
+    using System.Threading.Tasks;
+    using Microsoft.Azure.ServiceBus;
+    using NServiceBus.TransportTests;
+    using NUnit.Framework;
+
+    [TestFixture]
+    public class When_MessageLockLostException_is_thrown : NServiceBusTransportTest
+    {
+        [TestCase(TransportTransactionMode.None)]
+        [TestCase(TransportTransactionMode.ReceiveOnly)]
+        [TestCase(TransportTransactionMode.SendsAtomicWithReceive)]
+        public async Task Should_not_raise_critical_error(TransportTransactionMode transactionMode)
+        {
+            var criticalErrorInvoked = new TaskCompletionSource<bool>();
+            var criticalErrorCalled = false;
+
+            OnTestTimeout(() => criticalErrorInvoked.SetResult(false));
+
+            var firstInvocation = true;
+
+            await StartPump(
+                context =>
+                {
+                    if (firstInvocation)
+                    {
+                        firstInvocation = false;
+                        throw new MessageLockLostException("from onMessage");
+                    }
+
+                    return Task.CompletedTask;
+                },
+                context =>
+                {
+                    throw new MessageLockLostException("from onError");
+                },
+                transactionMode,
+                (message, exception) =>
+                {
+                    criticalErrorCalled = true;
+                    criticalErrorInvoked.SetResult(true);
+                }
+            );
+
+            await SendMessage(InputQueueName);
+
+            await criticalErrorInvoked.Task;
+
+            Assert.IsFalse(criticalErrorCalled, $"Should not invoke critical error for {nameof(MessageLockLostException)}");
+            Assert.IsFalse(criticalErrorInvoked.Task.Result);
+        }
+    }
+}
\ No newline at end of file
diff --git a/src/TransportTests/When_ServiceBusTimeoutException_is_thrown.cs b/src/TransportTests/When_ServiceBusTimeoutException_is_thrown.cs
new file mode 100644
index 00000000..1a19b571
--- /dev/null
+++ b/src/TransportTests/When_ServiceBusTimeoutException_is_thrown.cs
@@ -0,0 +1,54 @@
+namespace NServiceBus.Transport.AzureServiceBus.TransportTests
+{
+    using System.Threading.Tasks;
+    using Microsoft.Azure.ServiceBus;
+    using NServiceBus.TransportTests;
+    using NUnit.Framework;
+
+    [TestFixture]
+    public class When_ServiceBusTimeoutException_is_thrown : NServiceBusTransportTest
+    {
+        [TestCase(TransportTransactionMode.None)]
+        [TestCase(TransportTransactionMode.ReceiveOnly)]
+        [TestCase(TransportTransactionMode.SendsAtomicWithReceive)]
+        public async Task Should_not_raise_critical_error(TransportTransactionMode transactionMode)
+        {
+            var criticalErrorInvoked = new TaskCompletionSource<bool>();
+            var criticalErrorCalled = false;
+
+            OnTestTimeout(() => criticalErrorInvoked.SetResult(false));
+
+            var firstInvocation = true;
+
+            await StartPump(
+                context =>
+                {
+                    if (firstInvocation)
+                    {
+                        firstInvocation = false;
+                        throw new ServiceBusTimeoutException("from onMessage");
+                    }
+
+                    return Task.CompletedTask;
+                },
+                context =>
+                {
+                    throw new ServiceBusTimeoutException("from onError");
+                },
+                transactionMode,
+                (message, exception) =>
+                {
+                    criticalErrorCalled = true;
+                    criticalErrorInvoked.SetResult(true);
+                }
+            );
+
+            await SendMessage(InputQueueName);
+
+            await criticalErrorInvoked.Task;
+
+            Assert.IsFalse(criticalErrorCalled, $"Should not invoke critical error for {nameof(ServiceBusTimeoutException)}");
+            Assert.IsFalse(criticalErrorInvoked.Task.Result);
+        }
+    }
+}
\ No newline at end of file