Here's an image of a duplex canceller:
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By rule, the circular town/date canel had to be placed off the stamp(s) so as to be fully readable. The stamp(s) had to be canceled otherwise with a "killer".
So with this duplex cancel, everything could be done with one strike. Of course, if there was a strip of stamps on the cover, the clerk had to find a way to cancel all stamps without the circular part obliterating any stamps. One way of doing that was, as John Becker explained, slightly tilt the canceller so that only the "killer" would ink the stamp(s).