We improve some results of [JSz] and answer the main problem raised there. Thus we show that if a compact T_2 space X is not pseudoradial then there is a Y \subset X with |Y| < s so that the closure of Y is not pseudoradial. Also, we show that if any number of Cohen reals are added to a model of CH then CSC spaces are pseudoradial in the extension. As a byproduct, we also show that any \omega_1-compact and sequentially compact separable T_3 space is compact in such an extension.