We study supergravity solutions representing D3-branes with transverse 6-sp
ace having RxS(2)xS(3) topology. We consider regular and fractional D3-bran
es on a natural one-parameter extension of the standard Calabi-Yau metrics
on singular and resolved conifolds. After imposing a Z(2) identification on
an angular coordinate these generalized "6D conifolds" are nonsingular spa
ces. The back reaction of D3-branes creates a curvature singularity that co
incides with a horizon. In the presence of fractional D3-branes the solutio
ns are similar to the original ones by Klebanov and Tseytlin and Pando Zaya
s and Tseytlin: the metric has a naked repulson-type singularity located be
hind the radius where the 5-form flux vanishes. The semiclassical behavior
of the Wilson loop suggests that the corresponding gauge theory duals are c
onfining.