In the distributed edge-connectivity problem, every node in the distributed graph (the CONGEST model) needs to find what is the minimum number of edges required to be removed to disconnect the graph. This work addresses edge connectivity of constant size. Here, the first significant result was by [Pritchard and Thurimella, ACM TALG'2011], who gave a randomized algorithm that finds all the small sized cuts in O(D) time. Their algorithm is restrictive and finds cuts of size only one and two. The technique used here is binary random circulation. In this work, we resolve an open problem mentioned in Pritchard and Thurimella giving a deterministic algorithm for finding all cuts of size two in O(D) time. Our algorithm also improves results by Parter [DISC'19], who provided a fault-tolerant based approach to finding min-cuts poly(D, log n) (polynomial in the size of min-cut).