We study optimal timing of irreversible investment decisions under return and time uncertainty. The considered models are formulated as maximization problems of the expected present value of the exercise payoff, where the underlying dynamics follow a diffusion process. We formulate and study three variants of the benchmark model, namely the classical perpetual problem á-la Samuelson-McKean. Into each of these variants, we incorporate a different type of time uncertainty in terms of an exogenous Poissonian noise. For each variant, we propose a set of assumptions on the underlying and the payo? structure under which we can solve the timing problem. Furthermore, we study the interrelations of the timing problems and their interpretations. Finally, the results are illustrated with an explicit example.