A smooth submanifold whose inclusion has the same connectivity properties as the inclusion of a complex hypersurface is called taut. The diffeomorphism types of taut submanifolds are quite limited and a partial classification is obtained. The taut submanifolds are constructed using "ambient surgery". The obstruction to "ambient surgery" is calculated in terms of a cup product pairing on an eigen space of the cohomology of a certain branched covering space.