Cutting quantum computing's most expensive ingredient by 70%

T-gates are the bottleneck of fault-tolerant quantum computing — they're expensive and slow to implement on error-corrected hardware. This work generalizes a trick called phase kickback, previously confined to special circuit families, into a general-purpose tool that extracts favorable angle structures from any circuit and exploits them. Benchmarks show up to 70% fewer T-gates and 60% less space-time volume on real hardware layouts, though the two metrics sometimes diverge, warning that T-count alone can mislead optimization efforts.