This paper concerns the theory of morasses. In the early 1970s Jensen defined ($\kappa,\alpha$)-morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined ($\kappa$, 1)-simplified morasses for all regular cardinals $\kappa$. He showed that there is a ($\kappa$, 1)-simplified morass if and only if there is ($\kappa$, 1)-morass. More recently he defined ($\kappa$, 2)-simplified morasses and Jensen was able to show that if there is a ($\kappa$, 2)-morass then there is a ($\kappa$, 2)-simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a ($\kappa$, 2)-simplified morass then there is a ($\kappa$, 2)-morass.