MOTIVATION: Elucidating the functions of non-coding RNAs by homology has been strongly limited due to fundamental computational and modeling issues. While existing simultaneous alignment and folding (SA&F) algorithms successfully align homologous RNAs with precisely known boundaries (global SA&F), the more pressing problem of identifying new classes of homologous RNAs in the genome (local SA&F) is intrinsically more difficult and much less understood. Typically, the length of local alignments is strongly overestimated and alignment boundaries are dramatically mispredicted. We hypothesize that local SA&F approaches are compromised this way due to a score bias, which is caused by the contribution of RNA structure similarity to their overall alignment score. RESULTS: In the light of this hypothesis, we study pairwise local SA&F for the first time systematically-based on a novel local RNA alignment benchmark set and quality measure. First, we vary the relative influence of structure similarity compared to sequence similarity. Putting more emphasis on the structure component leads to overestimating the length of local alignments. This clearly shows the bias of current scores and strongly hints at the structure component as its origin. Second, we study the interplay of several important scoring parameters by learning parameters for local and global SA&F. The divergence of these optimized parameter sets underlines the fundamental obstacles for local SA&F. Third, by introducing a position-wise correction term in local SA&F, we constructively solve its principal issues. AVAILABILITY AND IMPLEMENTATION: The benchmark data, detailed results and scripts are available at https://github.com/BackofenLab/local_alignment. The RNA alignment tool LocARNA, including the modifications proposed in this work, is available at https://github.com/s-will/LocARNA/releases/tag/v2.0.0RC6. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.