Motivation: Template-based modelling can approximate the unknown structure of a target protein using an homologous template structure. The core of the resulting prediction then comprises the structural regions conserved between template and target. Target prediction could be improved by rigidly repositioning such single template, structurally conserved fragment regions. The purpose of this article is to quantify the extent to which such improvements are possible and to relate this extent to properties of the target, the template and their alignment. Results: The improvement in accuracy achievable when rigid fragments from a single template are optimally positioned was calculated using structure pairs from the HOMSTRAD database, as well as CASP7 and CASP8 target/best template pairs. Over the union of the structurally conserved regions, improvements of 0.7 Å in root mean squared deviation (RMSD) and 6% in GDT_HA were commonly observed. A generalized linear model revealed that the extent to which a template can be improved can be predicted using four variables. Templates with the greatest scope for improvement tend to have relatively more fragments, shorter fragments, higher percentage of helical secondary structure and lower sequence identity. Optimal positioning of the template fragments offers the potential for improving loop modelling. These results demonstrate that substantial improvement could be made on many templates if the conserved fragments were to be optimally positioned. They also provide a basis for identifying templates for which modification of fragment positions may yield such improvements.