A new shaper, the double gated-integrator, for shaping nuclear radiation detector signals is investigated both theoretically and experimentally. The double gated-integrator consists of a pre-filter and two cascaded gated integrators. Two kinds of pre-filters were considered: a rectangular one and an exponential one. The results of the theoretical calculation show that the best figure of demerit for the double gated-integrator with exponential pre-filter is 1.016. This means that its noise to signal ratio is only 1.6% worse than that it is for infinite cusp shaping. The practical realization of the exponential pre-filter and that of the double gated integrator, both in analogue and in digital way, is very simple. Therefore, the double gated-integrator with exponential pre-filter could be a promising solution for shaping nuclear radiation detector signals.