We hypothesize that the correct power counting for charmonia is in the para
meter A(QCD)/m(c), but is not based purely on dimensional analysis (as is h
eavy quark effective theory). This power counting leads to predictions whic
h differ from those resulting from the usual velocity power counting rules
of non-relativistic QCD (NRQCD). In particular, we show that while A(QCD)/m
(c), power counting preserves the empirically verified predictions of spin
symmetry in decays, it also leads to new predictions which include a hierar
chy between spin singlet and triplet octet matrix elements in the J/psi sys
tem, a quenching of the net polarization in production at large transverse
momentum, and no end point enhancement in radiative decays. We discuss expl
icit tests which can differentiate between the traditional and new theories
of NRQCD.