  We present a model for producing tidal streams from disrupting progenitors in
arbitrary potentials, utilizing the idea that the majority of stars escape from
the progenitor's two Lagrange points. The method involves releasing test
particles at the Lagrange points as the satellite orbits the host and
dynamically evolving them in the potential of both host and progenitor. The
method is sufficiently fast to allow large-dimensional parameter exploration
using Monte Carlo methods. We provide the first direct modelling of 6-D stream
observations -- assuming a stream rather than an orbit -- by applying our
methods to GD-1. This is a kinematically cold stream spanning $60^{\circ}$ of
the sky and residing in the outer Galaxy $\approx 15$ kpc distant from the
centre. We assume the stream moves in a flattened logarithmic potential
characterised by an asymptotic circular velocity $v_0$ and a flattening $q$. We
recover values of normalisation $v_0$ = $227.2^{+15.6}_{-18.2}$ kms$^{-1}$ and
flattening $q$ = $0.91^{+0.04}_{-0.1}$, if the stream is assumed to leading,
and $v_0$ = $226.5^{+17.9}_{-17.0}$ kms$^{-1}$, $q$ = $0.90^{+0.05}_{-0.09}$,
if it is assumed to be trailing. This can be compared to the values $v_0 = 224
\pm 13$ kms$^{-1}$ and $q= 0.87^{+0.07}_{-0.04}$ obtained by Koposov et al
(2010) using the simpler technique of orbit fitting. Although there are
differences between stream and orbit fitting, we conclude that orbit fitting
can provide accurate results given the current quality of the data, at least
for this kinematically cold stream in this logarithmic model of the Galaxy.
