The authors show that computing the value function for the \(d\)-time optimal stopping problem \[ v(S)= \text{ess\,sup}\{\operatorname{E}[\psi(\tau_1, \tau_2,\dots, \tau_d)|{\mathcal F}_S],\,\tau_1,\dots, \tau_d\in T_S\} \] reduces to computing the value function for an optimal single stopping time problem \[ v(S)= \text{ess\,sup}\{\operatorname{E}[\phi(\theta)|{\mathcal F}_S],\,\theta\in T_S\} \] a.s. for a reward \(\phi\) expressible in terms of optimal \((d-1)\)-stopping time problems, i.e., by induction, the initial optimal \(d\)-stopping time problem can be reduced to nested optimal single stopping time problems. Sufficient regularity of \(\psi\) assumed, \(\phi\) is shown to have a progressively measurable càdlàg modification, which opens a way for interesting applications, e.g., in finance.