We show how a static electric field can be used to control the localiz
ation of nonspreading wavepackets of a hydrogen atom driven by a linea
rly polarized microwave field. This allows for creation of wavepackets
localized on fully stable resonance islands which, at the same time,
can easily be excited by a direct optical transition from a low lying
state. A semiclassical analysis is used to predict the energies and pr
operties of such states.