Use a custom JSON converter on a list

Question

Let us say I have some data class

class MyData {
    public string SomeValue;
}

And I have a JsonConverter for this

class MyDataConverter : JsonConverter<MyData> {
    public override void WriteJson(JsonWriter writer, MyData value, 
        JsonSerializer serializer)
    {
        writer.WriteValue(value.SomeValue);
    }

    public override MyData ReadJson(JsonReader reader, Type objectType,
        MyData existingValue, bool hasExistingValue, JsonSerializer serializer) 
    {
        var readerValue = (string) reader.Value;
        return new MyData {SomeValue = readerValue};
    }
}

Now I can use this converter on classes containing instances of MyData. However, I can find no way to use this converter to convert instances of List<MyData>, e.g.

class ClassIWantToSerialize
{
    public List<MyData> SomeList;
}

Annotating [JsonConverter(typeof(MyDataConverter))] did not work (not surprisingly).

What would be the easiest way to go about this?