  Tidal streams are a powerful probe of the Milky Way (MW) potential shape. In
this paper, we introduce a simple test particle method to fit stream data,
using a Markov Chain Monte Carlo technique to marginalise over uncertainties in
the progenitor's orbit and the Milky Way halo shape parameters. Applying it to
mock data of thin streams in the MW halo, we show that, even for very cold
streams, stream-orbit offsets - not modelled in our simple method - introduce
systematic biases in the recovered shape parameters. For the streams that we
consider, and our particular choice of potential parameterisation, these errors
are of order ~20% on the halo flattening parameters. However, larger systematic
errors can arise for more general streams and potentials; such offsets need to
be correctly modelled in order to obtain an unbiased recovery of the underlying
potential.
  Assessing which of the known Milky Way streams are most constraining, we find
NGC 5466 and Pal 5 are the most promising candidates. These form an interesting
pair as their orbital planes are both approximately perpendicular to each other
and to the disc, giving optimal constraints on the MW halo shape. We show that
- while with current data their constraints on potential parameters are poor -
good radial velocity data along the Pal 5 stream will provide constraints on qz
- the flattening perpendicular to the disc. Furthermore, as discussed in a
companion paper, NGC 5466 can provide rather strong constraints on the MW halo
shape parameters, if the tentative evidence for a departure from the smooth
orbit towards its western edge is confirmed.
