SHAP scores represent one of the most widely used methods of explainability by feature attribution, as illustrated by the explainable AI tool SHAP. A number of recent works studied the computational complexity of the exact computation of SHAP scores, covering a comprehensive range of families of classifiers. This paper refines some of the existing complexity claims, including families of classifiers for which the computation of SHAP scores is computationally hard and those for which there exist polynomial-time algorithms.