We develop , implement and characterise an enhanced data reduction approach which delivers precise , accurate , radial velocities from moderate resolution spectroscopy with the fibre-fed VLT/FLAMES+GIRAFFE facility . This facility , with appropriate care , delivers radial velocities adequate to resolve the intrinsic velocity dispersions of the very faint dSph dwarf galaxies . Importantly , repeated measurements let us reliably calibrate our individual velocity errors ( 0.2 \leq \delta _ { V } \leq 5 km s ^ { -1 } ) and directly detect stars with variable radial velocities . We show , by application to the Boötes I dwarf spheroidal , that the intrinsic velocity dispersion of this system is significantly below 6.5 km/s reported by previous studies . Our data favor a two-population model of Boötes I , consisting of a majority ‘ cold ’ stellar component , with velocity dispersion 2.4 ^ { +0.9 } _ { -0.5 } km/s , and a minority ‘ hot ’ stellar component , with velocity dispersion \sim 9 km/s , although we can not completely rule out a single component distribution with velocity dispersion 4.6 ^ { 0.8 } _ { -0.6 } km/s . We speculate this complex velocity distribution actually reflects the distribution of velocity anisotropy in Boötes I , which is a measure of its formation processes .