The voltage-gated potassium channel Kv1.3 is an established target for treatment of autoimmune diseases. Hence, there are intense efforts to develop immunosuppressant drugs from Kv1.3 blockers. ShK toxin from sea anemone is the most advanced peptide in this regard, but its lack of selectivity for KvI.3 over Kv1.1 is an ongoing concern. The scorpion toxin HsTx1 is an equally potent blocker of Kv1.3, which is also selective for Kv1.3. It is of interest to understand the molecular basis of this selectivity as the lessons learned may suggest new avenues for enhancing the selectivity of other Kv1.3 blockers. Here we construct accurate models of Kv1.x HsTx1 complexes using docking and molecular dynamics simulations. For each complex, the binding free energy of HsTx1 is determined from the potential of mean force calculations. Good agreement is found between the computed and experimental binding free energies, which increases confidence in the complex models. Comparison of the binding modes of HsTx1 with Kv1.1 and Kv1.3 reveals that the lower affinity of HsTx1 for Kv1.1 is due to its inability to come close to the pore domain, which prevents the pore inserting lysine from making proper contacts with the tyrosine carbonyls in the selectivity filter.