Metallic nanoparticles behave as tiny antennas for light. Light illuminating such a particle can drive its mobile electrons into a collective oscillation called localized surface-plasmon resonances. The oscillating electronic current then emits light in certain directions determined by the size and geometry of the particle. The possibility they offer for the manipulation of light at nanoscales has been explored and exploited in several applications such as light emitting devices, optical sensors, and solar cells. There is a major challenge in such applications: the high losses associated with the damping of the electronic current by the material resistance and by the emission of light. In this paper of combined experimental and theoretical work on periodic arrays of metallic nanorods, we report our finding, and understanding, of a class of plasmonic resonances with very low losses—the lowest reported so far–and with additional desirable properties. The periodic arrays of metallic nanorods we have investigated diffract light in a similar way as optical gratings do: Beautiful rainbows are reflected or transmitted under white-light illumination. Therefore, light shone on such an array not only excites localized surface-plasmon resonances on the individual nanorods, but also gets diffracted in an ordered fashion. The diffracted light, in fact, is able to couple the localized surface-plasmon modes on the individual nanorods to each other. This coupling leads to resonances at a higher level: collective ones among the modes on the nanorods, known already as surface lattice resonances. What we have discovered and understood are the following: (1) by varying the angle of incidence of the illuminating light, collective lattice resonances of different frequencies can be excited, depending on the order of the diffracted light that underlies their individual emergences; (2) these collective lattice resonances are, in turn, also coupled to each other; (3) as a result of that coupling, lattice resonances of certain frequencies become forbidden, in other words, a frequency stop gap appears; (4) these lattice plasmonic modes suffer very low losses. These findings offer a new line of possibilities to tailor plasmonic resonances in a frequency-, angle-, and polarization-dependent manner in devices and also hold a promise for the development of low-loss plasmonic devices.