Transcription factors are a main component of gene regulation as they activate or repress gene expression by binding to specific binding sites in promoters. The de-novo discovery of transcription factor binding sites in target regions obtained by wet-lab experiments is a challenging problem in computational biology, which has not been fully solved yet. Here, we present a de-novo motif discovery tool called Dispom for finding differentially abundant transcription factor binding sites that models existing positional preferences of binding sites and adjusts the length of the motif in the learning process. Evaluating Dispom, we find that its prediction performance is superior to existing tools for de-novo motif discovery for 18 benchmark data sets with planted binding sites, and for a metazoan compendium based on experimental data from micro-array, ChIP-chip, ChIP-DSL, and DamID as well as Gene Ontology data. Finally, we apply Dispom to find binding sites differentially abundant in promoters of auxin-responsive genes extracted from Arabidopsis thaliana microarray data, and we find a motif that can be interpreted as a refined auxin responsive element predominately positioned in the 250-bp region upstream of the transcription start site. Using an independent data set of auxin-responsive genes, we find in genome-wide predictions that the refined motif is more specific for auxin-responsive genes than the canonical auxin-responsive element. In general, Dispom can be used to find differentially abundant motifs in sequences of any origin. However, the positional distribution learned by Dispom is especially beneficial if all sequences are aligned to some anchor point like the transcription start site in case of promoter sequences. We demonstrate that the combination of searching for differentially abundant motifs and inferring a position distribution from the data is beneficial for de-novo motif discovery. Hence, we make the tool freely available as a component of the open-source Java framework Jstacs and as a stand-alone application at http://www.jstacs.de/index.php/Dispom.