In Caro, Shapira and Yuster [Forcing k-repetitions in degree sequences, Electron. J. Combin. 21 (2014) #P1.24] it is proven that for any graph $G$ with at least $5$ vertices, one can delete at most $6$ vertices such that the subgraph obtained has at least three vertices with the same degree. Furthermore they show that for certain graphs one needs to remove at least $3$ vertices in order that the resulting graph has at least $3$ vertices of the same degree. In this note we prove that for any graph $G$ with at least $5$ vertices, one can delete at most $5$ vertices such that the subgraph obtained has at least three vertices with the same degree. We also show that for any triangle-free graph $G$ with at least $6$ vertices, one can delete at most one vertex such that the subgraph obtained has at least three vertices with the same degree and this result is tight for triangle-free graphs.