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 marginalize over uncertainties in the progenitor's orbit and the MW 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 parametrization, these errors are of the order of ∼20 per cent 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 MW streams are most constraining, we find that 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 q z - 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.