  If a finite group G has a presentation with d generators and r relations, it
is well-known that r - d is at least the rank of the Schur multiplier of G; a
presentation is called efficient if equality holds. There is an analogous
definition for proficient profinite presentations. We show that many perfect
groups have proficient presentations. Moreover, we prove that infinitely many
alternating groups, symmetric groups and their double covers have proficient
presentations
