  In this paper we study controllability of a linear equation with persistent
memory when the control belongs to $ H^k_0(0,T;L^2(\ZOMq)) $. In the case the
memory is zero, our equation is reduced to the wave equation and a result due
to Everdoza and Zuazua informally states that smoother targets can be reached
by using smoother controls. In this paper we prove that this result can be
partially extended to systems with memory, but that the memory is an
obstruction to a complete extensions.
