Abstract: Stop searches in supersymmetric frameworks with R-parity conservation usually assume the lightest neutralino to be the lightest supersymmetric particle. In this paper we consider an alternative scenario in which the left-handed tau sneutrino is lighter than neutralinos and stable at collider scales, but possibly unstable at cosmological scales. Moreover the (mostly right-handed) stop (t) over tilde is lighter than all electroweakinos, and heavier than the scalars of the third generation lepton doublet, whose charged component, (T) over tilde, is heavier than the neutral one, (v) over tilde. The remaining supersymmetric particles are decoupled from the stop phenomenology. In most of the parameter space, the relevant stop decays are only into t (T) over tildeT, t (v) over tildev and b (v) over tildeT via off-shell electroweakinos. We constrain the branching ratios of these decays by recasting the most sensitive stop searches. Due to the “double invisible” kinematics of the (t) over tilde -> t (v) over tildev process, and the low efficiency in tagging the t (T) over tildeT decay products, light stops are generically allowed. In the minimal supersymmetric standard model with similar to 100 GeV sneutrinos, stops with masses as small as similar to 350 GeV turn out to be allowed at 95% CL.