  We produce examples of taut foliations of hyperbolic 3-manifolds which are
R-covered but not uniform --- ie the leaf space of the universal cover is R,
but pairs of leaves are not contained in bounded neighborhoods of each other.
This answers in the negative a conjecture of Thurston `Three-manifolds,
foliations and circles I' (math.GT/9712268). We further show that these
foliations can be chosen to be C^0 close to foliations by closed surfaces. Our
construction underscores the importance of the existence of transverse
regulating vector fields and cone fields for R-covered foliations. Finally, we
discuss the effect of perturbing arbitrary R-covered foliations.
