  We study supergravity solutions representing D3-branes with transverse
6-space having R x S^2 x S^3 topology. We consider regular and fractional
D3-branes on a natural one-parameter extensions of the standard Calabi-Yau
metrics on the singular and resolved conifolds. After imposing a Z_2
identification on an angular coordinate these generalized "6-d conifolds" are
nonsingular spaces. The backreaction of D3-branes creates a curvature
singularity that coincides with a horizon. In the presence of fractional
D3-branes the solutions are similar to the original ones in hep-th/0002159,
hep-th/0010088: the metric has a naked repulson-type singularity located behind
the radius where the 5-form flux vanishes. The semiclassical behavior of the
Wilson loop suggests that the corresponding gauge theory duals are confining.
