Rim size/tyre size

My hybrid was on awful stock unbranded 700 x 37s and I have just ordered some Schwalbe Mountain Plus which are 700 x 35.
In retrospect, I was wondering whether I could have gone narrower ie a 32 or even a 28. Or would the rims on my bike have been too broad for narrower tyre?
In retrospect, I was wondering whether I could have gone narrower ie a 32 or even a 28. Or would the rims on my bike have been too broad for narrower tyre?
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Viner Maxima, Tifosi CK7, Giant Bowery, Old commuter.
Now I've checked that, I'm guessing the 32 is a clue?
Any idea what the narrowest tyre is that it will take?
I'm pretty sure 28s would be OK, but you wouldn't want to take my word for it.
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Gears - Obscuring the goodness of singlespeed
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Gears - Obscuring the goodness of singlespeed
Lesson learned :oops: !