Dear, there's nothing to be scared of, the officers are humans and they make mistakes too. They Know people can make mistakes. There are hundreds of questions to answer for a simple visa. Just be yourself and write the letter. The subject of the letter has to be Letter of explanation. and I don't know where you are from,if it was possible for you to get a police clearance from your country,it would be perfect, in your letter you could say you're a good citizen in your country, know and respect the laws and always act like a good citizen wherever you go. and the police clearance would be proof of that. but if you can't get the police clearance, just say and the letter you're sorry and the put the date of you past refusals.
and yes, i got the visa after writing the letter