Now that I'm on my laptop, I would say you definitely have 13x7 et-7 Mamba replicas. I'm still kind of curious what look you're going for. Do you want smaller wheels? Do you want smaller tires? Do you want smaller flares and then want to know what wheels will fill those out? I think we could probably help you out if you clarified what the actual goal was.

Looks like you have 13's now. Possibly 13x6 or 13x7. Really hard to tell by the pics though. Either way the offset is already likely very low. Your arches really look like sportspack. Those are fairly wide. I had them on my car for quite a while.

 I dont think the offset of a 13x7 with offset et-7 would put any more stress on the bearings than your current setup. And likely wouldn't change the steering much either compared to what you have. 

Here's my car with 13x7 et-7 wheels. Loved them and the look of them. 

Here's my car with 13x6 et +13. Different arches but nearly the same width. 

Here's another car with your arches and the same wheels I had. They won't be flush with the arches. Especially the rears. 

Looking at the pictures as far as i can see you have Sports pack type arches with what looks like reproduction Mamba's. Unless you are changing the arches which if going smaller would require bodywork you are going to need a 13 x 6 wheel which is what the factory fitted. Some owners go to a 13 x 7 wheel with massive off set which can create steering and premature wheel bearing problems. The least you could probably get away with is a 12 x 6 to fill those arches. Just measure the polished lip you have and go from there. There will be a much greater selection in the UK if you can't find what you want here.

I probably sound like a moron, I just don't know these cars well yet.  Just sold my Elise which I knew through and through.  Below is a link to my photo album with some pics of my car.  Its a 74 Morris with disc brakes at the front, drums on the rear.  It has arches as you can see in the pictures.  I'd like them to sit relativeley flush with the arches.  

//s592.photobucket.com/user/tylerwiggersvideo/library/Classic%20Mini?sort=3&page=1

Whether you are running discs or drums makes a difference too.

Post a picture of what you have currently.

I'm not trying to sound rude, but your question really is too vague. I can't tell you what offset is right because I don't know what look you're going for. Do you have flares? How wide of flare do you currently have? Do you want the wheels to sit inside the standard wheel arch? Do you want them to sit inside the flares you have now? Do you want them to poke out past the flare you have?

These would all be really helpful. But really..... you can figure this out by measuring things a bit for yourself. Whell offsets and backspacings are actually really simple. Make up a cardboard hoop with some coat hangers poking through and figure out where you want your wheels to sit. That's how I did it for years. haha. I'm working on something a bit fancier now, but it's still a really ugly useless prototype.

The very site you are posting your message to sells Mini wheels.

//www.minimania.com/BulkEmail_HTML.cfm?id=3504

I have a 1974 Morris and am looking for a set of MiniLite wheels for my 1974.  Does anyone know the correct  offset I would need?  And where the best place to buy them in the US is?  

The car is new-to-me (bought on Tuesday) and love it, just hate the wheels.