  We present a new efficient method to compute the angular power spectra of
large-scale structure observables that circumvents the numerical integration
over Bessel functions, expanding on a recently proposed algorithm based on
FFTlog. This new approach has better convergence properties. The method is
explicitly implemented in the CLASS code for the case of number count
$C_\ell$'s (including redshift-space distortions, weak lensing, and all other
relativistic corrections) and cosmic shear $C_\ell$'s. In both cases our
approach speeds up the calculation of the exact $C_\ell$'s (without the Limber
approximation) by a factor of order 400 at a fixed precision target of 0.1%.
