  We study contact manifolds that arise as cyclic branched covers of transverse
knots in the standard contact 3-sphere. We discuss properties of these contact
manifolds and describe them in terms of open books and contact surgeries. In
many cases we show that such branched covers are contactomorphic for smoothly
isotopic transverse knots with the same self-linking number. These pairs of
knots include most of the non-transversely simple knots of Birman-Menasco and
Ng-Ozsvath-Thurston.
