  This paper is concerned with the design and analysis of least squares solvers
for ill-posed PDEs that are conditionally stable. The norms and the
regularization term used in the least squares functional are determined by the
ingredients of the conditional stability assumption. We are then able to
establish a general error bound that, in view of the conditional stability
assumption, is qualitatively the best possible, without assuming consistent
data. The price for these advantages is to handle dual norms which reduces to
verifying suitable inf-sup stability. This, in turn, is done by constructing
appropriate Fortin projectors for all sample scenarios. The theoretical
findings are illustrated by numerical experiments.
