We investigate the interpolation spaces defined by Sparr and Fernandez's methods for 4-tuples Banach $\bar A=(A_0,A_1,A_2,A_3)$, where $A_i$ is of class $\mathcal C(\theta_i,X,Y)$. If $\theta_i$ is suitably chosen, then the $J$- and $K$- methods coincide and are equal to the space $(X,Y)_{\eta,p}$. Some concrete applications of this fact are also presented.