Group Algebras with Minimal Strong Lie Derived Length Let $KG$ be a non-commutative strongly Lie solvable group algebra of a group $G$ over a field $K$ of positive characteristic $p$. In this note we state necessary and sufficient conditions so that the strong Lie derived length of $KG$ assumes its minimal value, namely $\lceil \log_{2}(p+1)\rceil$. Keywords:group algebras, strong Lie derived lengthCategories:16S34, 17B30