Responding 1NT to Overcalls

"Sometimes, Watson, you can be a parcel of street dirt."
Holmes was being at his steeliest as he dissected a small - but I maintain, quite understandable - bidding error on my part.
"It's merely a question of thinking. This is what - sometimes - you just do not do. Calm, clear, rational though would lead you to the correct answer, even if you did not already know it."
"But, Holmes..." I squirmed, "you overcalled and I had 6 - 9 points, no fit, so responded 1NT! What can possibly be wrong there?"
"Almost everything" sighed the master. "And it is out of your own mouth that you are condemned. Consider: you said - correctly - that I overcalled, did you not?
"Er, ye - es..."
"Precisely. I overcalled! I did not OPEN. Therefore you cannot assume I hold "Opening" points, can you? However, you can assume that I hold, perhaps, at least as many as 3 points less than a normal opening bid. Therefore it is perfectly logical - is it not - that a response of 1NT to an overcall must of necessity contain at least 3 points MORE than the same response to an opening bid?"
"Do you mean to say that in response to an overcall, the bid of 1NT shows 9 - 12 HCP?"
"Indeed so, Watson. Indeed so. Perfectly logical, I would say..."