Measured neutron resonance cross sections are usually analyzed and parametrized by fitting theoretical curves to high-resolution point data. Theoretically, the cross sections depend mainly on the "internal" levels inside the fitted energy range but also on the "external" levels outside. Although the external levels are mostly unknown, they must be accounted for. If they are simply omitted, the experimental data cannot be fitted satisfactorily. Especially with elastic scattering and total cross-section data, one gets troublesome edge effects and difficulties with the potential cross section between resonances. Various ad hoc approaches to these problems are still being used, involving replacement of the unknown levels by equidistant ("picket fence") or Monte Carlo-sampled resonance sequences, or replication of the internal level sequence; however, more convenient, better working, and theoretically sound techniques have been available for decades. These analytical techniques are reviewed. They describe the contribution of external levels to the R matrix concisely in terms of average resonance parameters (strength function, effective radius, etc.). A more recent, especially convenient approximation accounts for the edge effects by just one fictitious pair of very broad external resonances. Fitting the thermal region, including accurately known thermal cross sections, is often done by adjusting a number of bound levels by trial and error, although again a simple analytical recipe involving just one bound level has been available for a long time. For illustration, these analytical techniques are applied to the resolved resonance region of 52Cr. The distinction between channel radii and effective radii, crucial in the present context, is emphasized.