Why can't I overload a method with the same parameters if I choose different general restrictions?

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private static void myMethod(int obj, IDictionary dictionary)
{
    // do something with the dictionary here, setting private members while you do it
}

private static void myMethod(int obj, ICollection collection)
{
    // do something with the collection here, setting private members while you do it
}

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private static void myMethodWithDictionary<T>(int obj) where T : IDictionary, new()
{
    // Create your new dictionary here, populate it, and set internal members
}

private static void myMethodWithCollection<T>(int obj) where T : ICollection, new()
{
    // Create your new collection here, populate it, and set internal members
}