  We reconsider the derivation of the nucleon-nucleon parity-violating (PV)
potential within a chiral effective field theory framework. We construct the
potential up to next-to-next-to-leading order by including one-pion-exchange,
two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use
dimensional regularization to renormalize the pion-loop corrections. A detailed
analysis of the number of independent low-energy constants (LEC's) entering the
potential is carried out. We find that it depends on six LEC's: the
pion-nucleon PV coupling constant $h^1_\pi$ and five parameters multiplying
contact interactions. We investigate PV effects induced by this potential on
several few-nucleon observables, including the $\vec{p}$-$p$ longitudinal
asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$
scattering, and the longitudinal asymmetry in the $^3$He$(\vec{n},p)^3$H
charge-exchange reaction. An estimate for the range of values of the various
LEC's is provided by using available experimental data.
