Summary: In this note, we revisit the problem of calculating small on-line Ramsey numbers \(\overline{\mathcal{R}}(G,H)\). A new approach is proposed that reduces the running time of the algorithm determining that \(\overline{\mathcal{R}}(K_3,K_4)=17\) by a factor of at least \(2\cdot 10^6\) comparing to the previously used approach. Using high performance computing networks, we determined that \(\overline{\mathcal{R}}(K_4,K_4) \geq 26\), \(\overline{\mathcal{R}}(K_3,K_5) \geq 25\), and that \(\overline{\mathcal{R}}(K_3,K_3,K_3) \geq 20\) for a natural generalization to three colours. All graphs on 3 or 4 vertices are investigated as well, including non-symmetric cases.