  We give a new and effective classification of all Borel Wadge classes of
subsets of Baire space. This relies on the true stage machinery originally
developed by Montalb\'an. We use this machinery to give a new proof of Louveau
and Saint-Raymond's separation theorem for Borel Wadge classes. This gives a
proof of Borel Wadge determinacy in the subsystem $\text{ATR}_0+\Pi^1_1$-I of
second-order arithmetic.
