  In the first of these two papers we demonstrated that assuming streams
delineate orbits can lead to order one errors in potential parameters for
realistic Galactic potentials. Motivated by the need for an improvement on
orbit-fitting, we now present an algorithm for constraining the Galactic
potential using tidal streams without assuming that streams delineate orbits.
This approach is independent of the progenitor mass so is valid for all
observed tidal streams. The method makes heavy use of angle-action variables
and seeks the potential which recovers the expected correlations in angle
space. We demonstrate that the method can correctly recover the parameters of a
simple two-parameter logarithmic potential by analysing an N-body simulation of
a stream. We investigate the magnitude of the errors in observational data for
which the method can still recover the correct potential and compare this to
current and future errors in data. The errors in the observables of individual
stars for current and near future data are shown to be too large for the direct
use of this method, but when the data are averaged in bins on the sky, the
resulting averaged data are accurate enough to constrain correctly the
potential parameters for achievable observational errors. From pseudo-data with
errors comparable to those that will be furnished in the era of Gaia (20 per
cent distance errors, 1.2 mas/yr proper motion errors, and 10 km/s
line-of-sight velocity errors) we recover the circular velocity, V_c=220 km/s,
and the flattening of the potential, q=0.9, to be V_c=223+/-10km/s and
q=0.91+/-0.09.
