Public pay-as-you-go pension systems are affected by sustainability problems due to the increasing longevity of the population. These problems come to light when there is unsustainable growth in pension expenditure in relation to GDP. The usual arrangement is for public systems to be complemented by private systems that provide a lifetime annuity paid alongside the public pension. This approach, which is horizontal in its way of thinking, is the one that all countries apply; in it, we can expect to find lifetime annuities, which are expensive because they have to take increasing longevity into account, as well as sustainability problems in the public accounts. Therefore, in this paper, we put forward a system that maintains the complementarity between private and public, but considers it from a vertical point of view. By this, we mean that over a certain period of time, the private system would provide the pension in the form of a temporary income, without the need to consider such a high longevity risk, and then in the following period, the public system would take over. We apply the model to Spain, one of the countries whose pension systems are most affected by problems of sustainability, and observe a decrease in the relationship between pension expenditure and GDP using this two-stage model as opposed to the current system, for the period 2025–2068. This decrease can be achieved without decrease of benefits, change in the retirement age or increase of the contribution level.