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We study curve-shortening flow for twisted curves in 
$\mathbb {R}^3$ (that is, curves with nowhere vanishing curvature 
$\kappa $ and torsion 
$\tau $) and define a notion of torsion-curvature entropy. Using this functional, we show that either the curve develops an inflection point or the eventual singularity is highly irregular (and likely impossible). In particular, it must be a Type-II singularity which admits sequences along which 
${\tau }/{\kappa ^2} \to \infty $. This contrasts strongly with Altschuler’s planarity theorem, which shows that 
${\tau }/{\kappa } \to 0$ along any essential blow-up sequence.
