In this paper optimal controller design which address the concerns of the H2 and the ℓ1 norms is studied. In the first problem a positive combination of the H2 and the ℓ1 norms of the closed loop is minimized. In the second the ℓ1 norm of a transfer function is minimized while restraining the another below a prespecified level. Converging upper and lower bounds are obtained. Relation to the pure ℓ1 problem is established. The solution methodology does not involve zero interpolation to characterize the achievable closed-loop maps. Thus obtaining the controller from the optimal closed-loop map is very straightforward.