We continue the study of freezing sets for digital images introduced in [L. Boxer and P.C. Staecker, Fixed point topology, 1, Applied General Topology 2020; L. Boxer, 2, Convexity Freezing Sets Digital Topology, 2021]. prove methods obtaining $(X,c_i)$ $X \subset \mathbb{Z}^2$ $i \in \{1,2\}$. give examples to show how these can lead determination minimal sets.