The σ -irregularity, a variant of the well-established Albertson irregularity, is a topological invariant defined for a graph G = ( V , E ) as σ ( G ) = ∑ u v ∈ E ( d ( u ) − d ( v ) ) 2 , where d ( u ) and d ( v ) denote the degrees of vertices u and v , respectively. Recent research has successfully characterized chemical trees with the maximum σ -irregularity. In this paper, we expand upon this research by establishing several structural properties of maximal trees with prescribed maximum degree Δ . Application of these properties enables us to characterize maximal trees with Δ = 5 . We establish that extremal trees contain only vertices of degrees 1 , 2 and Δ . Moreover, the number of edges with both end-vertices having the degree 2 or Δ is very small, so almost all edges have the (second) maximum possible contribution to σ -irregularity. We believe this property or similar should extend to maximal trees for any value of Δ , so this is an interesting direction for further research.