We discuss the interpretation of DNA profiles obtained from low template DNA samples. The most important challenge to interpretation in this setting arises when either or both of "drop-out" and "drop-in" create discordances between the crime scene DNA profile and the DNA profile expected under the prosecution allegation. Stutter and unbalanced peak heights are also problematic, in addition to the effects of masking from the profile of a known contributor. We outline a framework for assessing such evidence, based on likelihood ratios that involve drop-out and drop-in probabilities, and apply it to two casework examples. Our framework extends previous work, including new approaches to modelling homozygote drop-out and uncertainty in allele calls for stutter, masking and near-threshold peaks. We show that some current approaches to interpretation, such as ignoring a discrepant locus or reporting a "Random Man Not Excluded" (RMNE) probability, can be systematically unfair to defendants, sometimes extremely so. We also show that the LR can depend strongly on the assumed value for the drop-out probability, and there is typically no approximation that is useful for all values. We illustrate that ignoring the possibility of drop-in is usually unfair to defendants, and argue that under circumstances in which the prosecution relies on drop-out, it may be unsatisfactory to ignore any possibility of drop-in.