In previous work we discussed the integral-equation formalism for the computation of the structure of systems built through sequential addition, equilibration and irreversible quenching in place of individual particles. This sequential quenching model, appropriate for stow irreversible deposition, can be investigated by the techniques of equilibrium liquid theory. In the case of hard particles the problem is identical to that of random sequential addition. Our earlier calculations showed that the integral equation results for hard disks are in good agreement with simulation. In this paper we explore the structures arising from sequential quenching of square-well disks, which are found to be very different fi om those for the corresponding equilibrium case. The most interesting result is the much higher degree of clustering observed when particles are quenched one by one, as opposed to what is observed from the instantaneous quenching of an entire equilibrium system. (C) 2001 American Institute of Physics.