Cysteine (Cys) is regarded as the most conservative amino acid in nature, something that does not occur in the tunicate Oikopleura dioica, where this amino acid is one of the fastest evolving. In this work we analyze some of the causes of this intriguing absence of conservation. Considering the well-known stabilizing role of Cys, it was first investigated whether the lack of conservation was accompanied by an increase in intrinsic protein disorder. In contrast to expectations, it was found that O. dioica is the chordate that has the lowest levels of intrinsic disorder, while vertebrates (represented by Bos taurus) contain the most disordered proteins. Oikopleura proteins are shorter than their homologs in other Chordates (Ciona and B. taurus proteins are respectively 11% and 18% longer). This process of protein shortening was more intense in intrinsic disordered regions. As a result proteins became not only shorter but also more compact. It is also reported here that the conservation/divergence behavior of Cys depends on whether they are located in ordered or disordered regions. In the four species analyzed, disordered Cys are majorly (> 75%) not conserved at all. Ordered Cys instead, are much more free to diverge in Oikopleura than in the other chordates. We hypothesize that the preferential deletion of disordered regions resulted in a decreased protein disorder and a direct elimination (by deletion) of many ancestral Cys. Besides, the alterations (shortening or complete elimination) of some disordered regions (loops/random coils) probably promoted further Cys evolutionary volatility, because some ancestral Cys (and other amino acids which play a role in stability like Trp) located outside deleted regions became redundant due to the loss of their stabilizing partners.