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Thanks, scorpiojo and Toorak. But, Toorak, when I say I can't reconcile Neat with "pat", it doesn't really help a lot for you just to say "pat" = NEAT. I realise it has to equal NEAT, but I don't understand how/why it does. Similarly, just saying TIE for the clue "Support garment" and then changing it to TEE, without any explanation, doesn't really help either. I had thought of both TIE and TEE, but couldn't feel fully convinced by either. TEE is definitely a support, but it's not a garment on its own - to be a garment, it would seem to need the addition of another word to give TEE SHIRT, but TEE on its own surely isn't enough to be a garment?
It's not that I don't appreciate your trying to help, because I really do. But a little more justification of the parsing would be very welcome.