We study feedback control over erasure channels with packet-dropouts. To achieve robustness with respect to packet-dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. To reduce the data size of packets, we propose to adopt sparsity-promoting optimizations, namely, l(1)-l(2) and l(2)-constrained l(0) optimizations, for which efficient algorithms exist. We show how to design the tuning parameters to ensure (practical) stability of the resulting feedback control systems when the number of consecutive packet-dropouts is bounded.