We recalculate in a systematic and pedagogical way one of the most important results in the light-cone formulation of Bosonic open string theory, namely the [J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously yield the critical dimension D=26 and the normal order constant a=1. We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter kappa to avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.