Decyphering a town name

Butch Hill

I have located immigration records (ship manifests) for three of my
direct ancestors. I had hoped to be able to determine their town of
origin from the 'Last Residence' field, but the information doesn't
seem to readily idenfity one of the many names contained within
JewishGen. I think the town is located within the Minsk Gubernia as
that is where all of these folks were from. I also suspect it's
somewhere in the vicinity of Nyasvich. Below are the three spellings
from the software that reads the images. I think it's the same town
with different spellings. So far, my best guess is Sverzhen' Novy, but
it's just a guess. Any chance someone familiar with the languages
could lend assistance?

From a Rotterdam manifest - Twersny (Note: the 'T' is unreadable on
the original image)
From a Hamburg manifest - Swersne
From a Hamburg manifest - Szweszne

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