diff --git a/src/DotNext.Tests/Threading/Tasks/ConversionTests.cs b/src/DotNext.Tests/Threading/Tasks/ConversionTests.cs
index b66ca9599..037c18904 100644
--- a/src/DotNext.Tests/Threading/Tasks/ConversionTests.cs
+++ b/src/DotNext.Tests/Threading/Tasks/ConversionTests.cs
@@ -55,4 +55,12 @@ public static async Task SuspendException2()
         var result = await t.AsDynamic().ConfigureAwait(ConfigureAwaitOptions.SuppressThrowing | ConfigureAwaitOptions.ContinueOnCapturedContext);
         Same(result, Missing.Value);
     }
+    
+    [Fact]
+    public static async Task SuspendExceptionParametrized()
+    {
+        await Task.FromException(new Exception()).SuspendException(42, (_, i) => i is 42);
+        await ValueTask.FromException(new Exception()).SuspendException(42, (_, i) => i is 42);
+        await ThrowsAsync<Exception>(async () => await Task.FromException(new Exception()).SuspendException(43, (_, i) => i is 42));
+    }
 }
\ No newline at end of file
diff --git a/src/DotNext.Threading/Threading/Tasks/TaskQueue.cs b/src/DotNext.Threading/Threading/Tasks/TaskQueue.cs
index 18e92f1ff..3c1aa4f7e 100644
--- a/src/DotNext.Threading/Threading/Tasks/TaskQueue.cs
+++ b/src/DotNext.Threading/Threading/Tasks/TaskQueue.cs
@@ -178,7 +178,7 @@ public async ValueTask EnqueueAsync(T task, CancellationToken token = default)
         }
     }
 
-    private T? TryPeekOrDequeue(out int head, out Task enqueueTask, out bool completed)
+    private T? TryPeekOrDequeue(out int head, out Task enqueueTask)
     {
         T? result;
         lock (array)
@@ -187,7 +187,7 @@ public async ValueTask EnqueueAsync(T task, CancellationToken token = default)
             {
                 result = this[head = this.head];
                 enqueueTask = Task.CompletedTask;
-                if (completed = result is { IsCompleted: true })
+                if (result is { IsCompleted: true })
                 {
                     MoveNext(ref head);
                     ChangeCount(increment: false);
@@ -197,7 +197,6 @@ public async ValueTask EnqueueAsync(T task, CancellationToken token = default)
             {
                 head = default;
                 result = null;
-                completed = default;
                 signal ??= new();
                 enqueueTask = signal.Task;
             }
@@ -258,17 +257,17 @@ public bool TryDequeue([NotNullWhen(true)] out T? task)
     /// <exception cref="OperationCanceledException">The operation has been canceled.</exception>
     public async ValueTask<T> DequeueAsync(CancellationToken token = default)
     {
-        for (var filter = token.CanBeCanceled ? null : Predicate.Constant<Exception>(true);;)
+        for (;;)
         {
-            if (TryPeekOrDequeue(out var expectedHead, out var enqueueTask, out var completed) is not { } task)
+            if (TryPeekOrDequeue(out var expectedHead, out var enqueueTask) is not { } task)
             {
                 await enqueueTask.WaitAsync(token).ConfigureAwait(false);
                 continue;
             }
 
-            if (!completed)
+            if (!task.IsCompleted)
             {
-                await task.WaitAsync(token).SuspendException(filter ??= token.SuspendAllExceptCancellation).ConfigureAwait(false);
+                await task.WaitAsync(token).SuspendException(token, SuspendAllExceptCancellation).ConfigureAwait(false);
 
                 if (!TryDequeue(expectedHead, task))
                     continue;
@@ -286,12 +285,12 @@ public async ValueTask<T> DequeueAsync(CancellationToken token = default)
     /// <exception cref="OperationCanceledException">The operation has been canceled.</exception>
     public async ValueTask<T?> TryDequeueAsync(CancellationToken token = default)
     {
-        for (var filter = token.CanBeCanceled ? null : Predicate.Constant<Exception>(true);;)
+        for (;;)
         {
             T? task;
-            if ((task = TryPeekOrDequeue(out var expectedHead, out _, out var completed)) is not null && !completed)
+            if ((task = TryPeekOrDequeue(out var expectedHead, out _)) is not null && !task.IsCompleted)
             {
-                await task.WaitAsync(token).SuspendException(filter ??= token.SuspendAllExceptCancellation).ConfigureAwait(false);
+                await task.WaitAsync(token).SuspendException(token, SuspendAllExceptCancellation).ConfigureAwait(false);
 
                 if (!TryDequeue(expectedHead, task))
                     continue;
@@ -311,12 +310,11 @@ public async ValueTask<T> DequeueAsync(CancellationToken token = default)
     /// <returns>The enumerator over completed tasks.</returns>
     public async IAsyncEnumerator<T> GetAsyncEnumerator(CancellationToken token)
     {
-        for (var filter = token.CanBeCanceled ? null : Predicate.Constant<Exception>(true);
-             TryPeekOrDequeue(out var expectedHead, out _, out var completed) is { } task;)
+        while (TryPeekOrDequeue(out var expectedHead, out _) is { } task)
         {
-            if (!completed)
+            if (!task.IsCompleted)
             {
-                await task.WaitAsync(token).SuspendException(filter ??= token.SuspendAllExceptCancellation).ConfigureAwait(false);
+                await task.WaitAsync(token).SuspendException(token, SuspendAllExceptCancellation).ConfigureAwait(false);
                 if (!TryDequeue(expectedHead, task))
                     continue;
             }
@@ -325,6 +323,9 @@ public async IAsyncEnumerator<T> GetAsyncEnumerator(CancellationToken token)
         }
     }
 
+    private static bool SuspendAllExceptCancellation(Exception e, CancellationToken token)
+        => e is not OperationCanceledException canceledEx || token != canceledEx.CancellationToken;
+
     /// <summary>
     /// Clears the queue.
     /// </summary>
@@ -343,10 +344,4 @@ public void Clear()
     void IResettable.Reset() => Clear();
 
     private sealed class Signal() : TaskCompletionSource(TaskCreationOptions.RunContinuationsAsynchronously);
-}
-
-file static class CancellationTokenExtensions
-{
-    internal static bool SuspendAllExceptCancellation(this object token, Exception e)
-        => e is not OperationCanceledException canceledEx || !canceledEx.CancellationToken.Equals(token);
 }
\ No newline at end of file
diff --git a/src/DotNext/Runtime/CompilerServices/SuspendedExceptionTaskAwaitable.cs b/src/DotNext/Runtime/CompilerServices/SuspendedExceptionTaskAwaitable.cs
index 6ec23a437..de636f575 100644
--- a/src/DotNext/Runtime/CompilerServices/SuspendedExceptionTaskAwaitable.cs
+++ b/src/DotNext/Runtime/CompilerServices/SuspendedExceptionTaskAwaitable.cs
@@ -1,3 +1,4 @@
+using System.Diagnostics;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
 
@@ -15,7 +16,9 @@ internal SuspendedExceptionTaskAwaitable(ValueTask task)
         => this.task = task;
 
     internal SuspendedExceptionTaskAwaitable(Task task)
-        => this.task = new(task);
+        : this(new ValueTask(task))
+    {
+    }
 
     internal bool ContinueOnCapturedContext
     {
@@ -91,4 +94,97 @@ public void GetResult()
             }
         }
     }
+}
+
+/// <summary>
+/// Represents awaitable object that can suspend exception raised by the underlying task.
+/// </summary>
+/// <typeparam name="TArg">The type of the argument to be passed to the exception filter.</typeparam>
+[StructLayout(LayoutKind.Auto)]
+public readonly struct SuspendedExceptionTaskAwaitable<TArg>
+{
+    private readonly TArg arg;
+    private readonly ValueTask task;
+    private readonly Func<Exception, TArg, bool> filter;
+
+    internal SuspendedExceptionTaskAwaitable(ValueTask task, TArg arg, Func<Exception, TArg, bool> filter)
+    {
+        Debug.Assert(filter is not null);
+        
+        this.task = task;
+        this.arg = arg;
+        this.filter = filter;
+    }
+
+    internal SuspendedExceptionTaskAwaitable(Task task, TArg arg, Func<Exception, TArg, bool> filter)
+        : this(new ValueTask(task), arg, filter)
+    {
+    }
+
+    internal bool ContinueOnCapturedContext
+    {
+        get;
+        init;
+    }
+
+    /// <summary>
+    /// Configures an awaiter for this value.
+    /// </summary>
+    /// <param name="continueOnCapturedContext">
+    /// <see langword="true"/> to attempt to marshal the continuation back to the captured context;
+    /// otherwise, <see langword="false"/>.
+    /// </param>
+    /// <returns>The configured object.</returns>
+    public SuspendedExceptionTaskAwaitable<TArg> ConfigureAwait(bool continueOnCapturedContext)
+        => this with { ContinueOnCapturedContext = continueOnCapturedContext };
+
+    /// <summary>
+    /// Gets the awaiter for this object.
+    /// </summary>
+    /// <returns>The awaiter for this object.</returns>
+    public Awaiter GetAwaiter() => new(task, arg, filter, ContinueOnCapturedContext);
+
+    /// <summary>
+    /// Represents the awaiter that suspends exception.
+    /// </summary>
+    [StructLayout(LayoutKind.Auto)]
+    public readonly struct Awaiter : ICriticalNotifyCompletion
+    {
+        private readonly ConfiguredValueTaskAwaitable.ConfiguredValueTaskAwaiter awaiter;
+        private readonly TArg arg;
+        private readonly Func<Exception, TArg, bool> filter;
+
+        internal Awaiter(in ValueTask task, TArg arg, Func<Exception, TArg, bool> filter, bool continueOnCapturedContext)
+        {
+            awaiter = task.ConfigureAwait(continueOnCapturedContext).GetAwaiter();
+            this.arg = arg;
+            this.filter = filter;
+        }
+
+        /// <summary>
+        /// Gets a value indicating that <see cref="SuspendedExceptionTaskAwaitable"/> has completed.
+        /// </summary>
+        public bool IsCompleted => awaiter.IsCompleted;
+
+        /// <inheritdoc/>
+        public void OnCompleted(Action action) => awaiter.OnCompleted(action);
+
+        /// <inheritdoc/>
+        public void UnsafeOnCompleted(Action action) => awaiter.UnsafeOnCompleted(action);
+
+        /// <summary>
+        /// Obtains a result of asynchronous operation, and suspends exception if needed.
+        /// </summary>
+        public void GetResult()
+        {
+            try
+            {
+                awaiter.GetResult();
+            }
+            catch (Exception e) when (filter.Invoke(e, arg))
+            {
+                // suspend exception
+            }
+        }
+    }
 }
\ No newline at end of file
diff --git a/src/DotNext/Threading/Tasks/Conversion.cs b/src/DotNext/Threading/Tasks/Conversion.cs
index 0283f4fcd..daa2c5498 100644
--- a/src/DotNext/Threading/Tasks/Conversion.cs
+++ b/src/DotNext/Threading/Tasks/Conversion.cs
@@ -3,7 +3,7 @@
 
 namespace DotNext.Threading.Tasks;
 
-using SuspendedExceptionTaskAwaitable = Runtime.CompilerServices.SuspendedExceptionTaskAwaitable;
+using Runtime.CompilerServices;
 
 /// <summary>
 /// Provides task result conversion methods.
@@ -84,4 +84,32 @@ public static SuspendedExceptionTaskAwaitable SuspendException(this Task task, P
     /// <returns>The awaitable object that suspends exceptions according to the filter.</returns>
     public static SuspendedExceptionTaskAwaitable SuspendException(this ValueTask task, Predicate<Exception>? filter = null)
         => new(task) { Filter = filter };
+
+    /// <summary>
+    /// Suspends the exception that can be raised by the task.
+    /// </summary>
+    /// <param name="task">The task.</param>
+    /// <param name="arg">The argument to be passed to the filter.</param>
+    /// <param name="filter">The filter of the exception to be suspended.</param>
+    /// <returns>The awaitable object that suspends exceptions according to the filter.</returns>
+    public static SuspendedExceptionTaskAwaitable<TArg> SuspendException<TArg>(this Task task, TArg arg, Func<Exception, TArg, bool> filter)
+    {
+        ArgumentNullException.ThrowIfNull(filter);
+        
+        return new(task, arg, filter);
+    }
+
+    /// <summary>
+    /// Suspends the exception that can be raised by the task.
+    /// </summary>
+    /// <param name="task">The task.</param>
+    /// <param name="arg">The argument to be passed to the filter.</param>
+    /// <param name="filter">The filter of the exception to be suspended.</param>
+    /// <returns>The awaitable object that suspends exceptions according to the filter.</returns>
+    public static SuspendedExceptionTaskAwaitable<TArg> SuspendException<TArg>(this ValueTask task, TArg arg, Func<Exception, TArg, bool> filter)
+    {
+        ArgumentNullException.ThrowIfNull(filter);
+        
+        return new(task, arg, filter);
+    }
 }
\ No newline at end of file