This paper answers some questions of D. Ross in [R]. In $\S 1$, we show that some consequences of the $\aleph_0$- or $\aleph_1$-special model axiom in [R] cannot be proved by the $\kappa$-isomorphism property for any cardinal $\kappa$. In $\S 2$, we show that with one exception, the $\aleph_0$-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In $\S 3$, we improve a result in [R] by showing that the $\kappa$-special model axiom is equivalent to the $\aleph_0$-special model axiom plus $\kappa$-saturation.