  Decoupling the interactions in a spin network governed by a pair-interaction
Hamiltonian is a well-studied problem. Combinatorial schemes for decoupling and
for manipulating the couplings of Hamiltonians have been developed which use
selective pulses. In this paper we consider an additional requirement on these
pulse sequences: as few {\em different} control operations as possible should
be used. This requirement is motivated by the fact that optimizing each
individual selective pulse will be expensive, i. e., it is desirable to use as
few different selective pulses as possible. For an arbitrary $d$-dimensional
system we show that the ability to implement only two control operations is
sufficient to turn off the time evolution. In case of a bipartite system with
local control we show that four different control operations are sufficient.
Turning to networks consisting of several $d$-dimensional nodes which are
governed by a pair-interaction Hamiltonian, we show that decoupling can be
achieved if one is able to control a number of different control operations
which is logarithmic in the number of nodes.
