Let \(T \in \varSigma ^n\) be a text over alphabet \(\varSigma \) . A suffixient set \(\mathcal {S} \subseteq [n]\) for T is a set of positions such that, for every one-character right-extension T[i, j] of every right-maximal substring \(T[i,j-1]\) of T, there exists \(x\in S\) such that T[i, j] is a suffix of T[1, x]. It was recently shown that, given a suffixient set of cardinality q and an oracle offering fast random access on T (for example, a straight-line program), there is a data structure of O(q) words (on top of the oracle) that can quickly find all Maximal Exact Matches (MEMs) of any query pattern P in T with high probability. The paper introducing suffixient sets left open the problem of computing the smallest such set; in this paper, we solve this problem by describing a simple quadratic-time algorithm, a \(O(n + \bar{r}|\varSigma |)\) -time algorithm running in compressed working space ( \(\bar{r}\) is the number of runs in the Burrows-Wheeler transform of T reversed), and an optimal O(n)-time algorithm computing the smallest suffixient set. We present an implementation of our compressed-space algorithm and show experimentally that it uses a small memory footprint on repetitive text collections.