Thin, metallic magnetic films can support nonreciprocal spin waves due to the interfacial Dzyaloshinskii-Moriya interaction (iDMI). However, these films typically have high damping, making spin wave propagation distances short (less than one micrometer). In this work, we theoretically study a thin ferromagnetic strip with iDMI and excite spin waves by driving a central segment of the strip. Spin waves propagate with different amplitudes to the left versus to the right from the driving region (i.e. nonreciprocity occurs) due to the iDMI. Our calculation based on spin-wave-dispersion plus our micromagnetic simulations both show that changing the driving segment width, driving frequency and static applied field strength tunes the nonreciprocity. Our calculation based on spin-wave-dispersion, using a so-called ``overlap function" will allow researchers to predict conditions of maximum nonreciprocity, without the need for computational solvers. Moreover, to circumvent the issue of short propagation distances, we propose a geometry where iDMI is only present in the driving region and low-damping materials comprise the remainder of the strip. Our calculations show significant spin wave amplitudes over several microns from the excitation region.