  We calculate the (parity-violating) spin rotation angle of a polarized
neutron beam through hydrogen and deuterium targets, using pionless effective
field theory up to next-to-leading order. Our result is part of a program to
obtain the five leading independent low-energy parameters that characterize
hadronic parity-violation from few-body observables in one systematic and
consistent framework. The two spin-rotation angles provide independent
constraints on these parameters. Using naive dimensional analysis to estimate
the typical size of the couplings, we expect the signal for standard target
densities to be 10^-7 to 10^-6 rad/m for both hydrogen and deuterium targets.
We find no indication that the nd observable is enhanced compared to the np
one. All results are properly renormalized. An estimate of the numerical and
systematic uncertainties of our calculations indicates excellent convergence.
An appendix contains the relevant partial-wave projectors of the three-nucleon
system.
