We consider D3 branes at orbifolded conifold singularities which are not qu
otient singularities. We use toric geometry to study the moduli space of th
e gauge theories on the D3 branes. We find that topologically distinct phas
es are related by a flop transition. It is also shown how the conifold sing
ularity is partially solved to an orbifold singularity in some phases if we
give expectation values to some of the chiral fields.