This note studies stabilization problems arising in discrete estimation (or preview tracking) problems when unstable exosystems are used to impose steady-state behavior constraints. The main theme is stabilizability conditions under FIR (finite impulse response) constraints. Necessary and sufficient stabilizability conditions are derived and all solutions are parametrized. Unlike the continuous-time case, where the problem is solvable under the standard detectability condition, stabilizability in the discretetime case depends on the length of the impulse response and, sometimes, also on the smoothing lag (length of preview). (c) 2012 Elsevier Ltd. All rights reserved.