While regular W-algebras have enjoyed many years of study and attention, recent developments in physics have the less popular subregular W-algebras playing an important role. Moreover, these subregular W-algebras appear at levels where the corresponding conformal field theory is likely non-rational. This necessitates a deeper understanding of the representation theory of such vertex operator algebras at non-rational levels. In type A_n, only the n=1 (sl_2) and n=2 (Bershadsky-Polyakov algebra) cases are particularly well-understood. In both cases an 'inverse reduction-by-stages' approach, first described for sl_2 in vertex operator algebra language by D. Adamovic, relates much of the representation theory to that of the corresponding regular W-algebra. In this talk, I will describe how to generalise this approach to all type A_n subregular W-algebras using screening operators developed by N. Genra.