  We show how to construct consistent braneworld models which exhibit late time
acceleration. Unlike self-acceleration, which has a de Sitter vacuum state, our
models have the standard Minkowski vacuum and accelerate only in the presence
of matter, which we dub ``stealth-acceleration''. We use an effective action
for the brane which includes an induced gravity term, and allow for an
asymmetric set-up. We study the linear stability of flat brane vacua and find
the regions of parameter space where the set-up is stable. The 4-dimensional
graviton is only quasi-localised in this set-up and as a result gravity is
modified at late times. One of the two regions is strongly coupled and the
scalar mode is eaten up by an extra symmetry that arises in this limit. Having
filtered the well-defined theories we then focus on their cosmology. When the
graviton is quasi-localised we find two main examples of acceleration. In each
case, we provide an illustrative model and compare it to LambdaCDM.
