static class Bar {
    public static string MightThrowException(int i) {
        if (i == 2) throw new Exception("bad error: " + i.ToString());
        // if not 2, just return input
        return i.ToString();
    }
}

public async Task<string> TestThrottle() {
    var tasks = new List<Task<string>>();
    var results = new List<string>();

    // mock the 'priming' that occurs in a throttling pattern
    tasks.Add(Task.Run(() => Bar.MightThrowException(0)));

    // begin throttling, for an additional 4 tasks
    for (var i = 1; i < 5; i++) {
        try {
            var task = await Task.WhenAny(tasks);
            results.Add(task.Result);
            tasks.Remove(task);
        }
        catch (Exception ex) {
            results.Add("handled " + ex.Message);
        }
        tasks.Add(Task.Run(() => Bar.MightThrowException(i)));
    }

    return string.Join("n", results);
}

Task.Run(() => {
    string result = new Foo().TestThrottle().Result;
    System.Diagnostics.Debug.WriteLine(result);
}).Wait();

tasks.Add(Task.Run(() => Bar.MightThrowException(i)));