In recent years many studies into green solvents have been undertaken and deep eutectic solvents (DES) have emerged as sustainable and green alternatives to conventional solvents since they may be formed from cheap non-toxic organic precursors. In this study we examine amphiphile behaviour in these novel media to test our understanding of amphiphile self-assembly within environments that have an intermediate polarity between polar and non-polar extremes. We have built on our recently published results to present a more detailed structural characterisation of micelles of sodium dodecylsulfate (SDS) within the eutectic mixture of choline chloride and urea. Here we show that SDS adopts an unusual cylindrical aggregate morphology, unlike that seen in water and other polar solvents. A new morphology transition to shorter aggregates was found with increasing concentration. The self-assembly of SDS was also investigated in the presence of water; which promotes the formation of shorter aggregates.