tramp ssh login fails when not prompted for password

[Jacob Smulllyan]

Hi --

I've read the info manual, but I seem to be missing something which must be very
basic.  Forgive me if this is an old chestnut.

When I have an ssh key which permits me to login to a server without being
prompted for a password, tramp, in its virgin, unconfigured state, believes that
the login has failed.  How do I tell tramp that it shouldn't expect a password
from a given server?

Thanks,

Jacob Smullyan
Tramp, Neophyte, and Tramp Neophyte