The neutron current density can be increased by using a converging guide; this can be particularly useful as the last section of a long straight guide. We give the expected flux gains for such a system. This increased density is obtained at the expense of increased divergence of the beam, which is unimportant in neutron absorption techniques, such as prompt gamma activation analysis and neutron depth profiling. These experiments can benefit from improved detection limits available when the neutron beam is focused by a neutron optical element such as a converging guide.