  We use two truly canonical approaches to describe superconductivity in
ultrasmall metallic grains: (a) a variational fixed-N projected BCS-like theory
and (b) an exact solution of the model Hamiltonian developed by Richardson in
context with Nuclear Physics. Thereby we obtain a description of the entire
crossover from the bulk BCS regime (mean level spacing $d\ll$ bulk gap
$\tilde\Delta$) to the `fluctuation-dominated' few-electron regime
($d\gg\tilde\Delta$). A wave-function analysis shows in detail how the BCS
limit is recovered and how for $d\gg\tilde\Delta$ pairing correlations become
delocalized in energy space.
