This paper presents an approach for designing out-of-ecliptic orbits for infrared (IR) space-borne observatories. A large displacement normal to the ecliptic plane mitigates the noise generated by the local zodiacal dust, thereby reducing the size, weight and complexity of the telescope. While previous works focused on long-term missions, for which transfers to out-of-ecliptic orbits are allowed to be very long, this paper considers relatively short-duration missions, for which the programmatic constraints are more pronounced. In order to reduce energy requirements, an optimal multiple gravity-assisted trajectory is designed. To reduce the transfer time, the flyby sequence includes the inner planets only: Venus, Earth and Mars. The problem is modeled using the patched-conic approximation and solved using a hybrid genetic-algorithm coupled to a pattern search. Efficient trajectories requiring a minimum velocity addition while providing a maximum observation time are found and validated using an N-body simulation. The TPF-I mission is used as benchmark in order to quantify the systematic benefits of an out-of-ecliptic orbit. It is shown that the newly-found orbits are very promising for IR missions, as they allow a considerable reduction in the collector area and the concomitant cost per image.