I will discuss a mechanism which can lead to a possible instability of the KKLT construction for de Sitter vacua. The sphere at the tip of a warped deformed conifold throat can be destabilized by antibranes placed in the throat. Consequently, the stabilization of moduli should not be treated independently from the antibrane uplift in KKLT-like scenarios. This conifold destabilization mechanism can be avoided by turning on a large amount of flux on the sphere, but tadpole cancelation constraints the hierarchy of scales in a type IIB flux compactification. This indicates that antibrane uplift cannot be used to construct stable de Sitter vacua with a small cosmological constant in perturbative string theory.