In recent years statistical models for the analysis of complex (low-template and/or mixed) DNA profiles have moved from using only presence/absence information about allelic peaks in an electropherogram, to quantitative use of peak heights. This is challenging because peak heights are very variable and affected by a number of factors. We present a new peak-height model with important novel features, including over- and double-stutter, and a new approach to dropin. Our model is incorporated in open-source R code likeLTD . We apply it to 108 laboratory-generated crime-scene profiles and demonstrate techniques of model validation that are novel in the field. We use the results to explore the benefits of modeling peak heights, finding that it is not always advantageous, and to assess the merits of pre-extraction replication. We also introduce an approximation that can reduce computational complexity when there are multiple low-level contributors who are not of interest to the investigation, and we present a simple approximate adjustment for linkage between loci, making it possible to accommodate linkage when evaluating complex DNA profiles.