  We introduce a novel strategy for cosmological Boltzmann codes leading to an
increase in speed by a factor of \sim 30 for small scale Fourier modes. We
(re-)investigate the tight coupling approximation and obtain analytic formulae
reaching up to the octupoles of photon intensity and polarization. This leads
to accurate results reaching optimal precision, while still being simple.
Damping rapid oscillations of small scale modes at later times, we simplify the
integration of cosmological perturbations. We obtain analytic expressions for
the photon density contrast and velocity as well as an estimate of the
quadrupole from after last scattering until today. These analytic formulae hold
well during re-ionization and are in fact negligible for realistic cosmological
scenarios. However, they do extend the validity of our approach to models with
very large optical depth to the last scattering surface.
