The Illumina NexteraXT transposon protocol is a cost effective way to generate paired end libraries. However the resulting insert size is highly sensitive to the concentration of DNA used, and the variation of insert sizes is often large. One consequence of this is some fragments may have an insert shorter than the length of a single read, particularly where the library is designed to produce overlapping paired end reads in order to produce longer continuous sequences. Such small insert sizes mean fewer longer reads, and also result in the presence of adapter at the end of the read. Here is presented a protocol to use publicly available tools to identify read pairs with small insert sizes and so likely to contain adapter, to check the sequence of the adapter, and remove adapter sequence from the reads. This protocol does not require a reference genome or prior knowledge of the sequence to be trimmed. Whilst the presence of fragments with small insert sizes may be a particular problem for NexteraXT libraries, the principle can be applied to any Illumina dataset in which the presence of such small inserts is suspected.