  We assess the effects of an intrinsic model for imperfections in cluster
states by introducing {\it noisy cluster states} and characterizing their role
in the one-way model for quantum computation. The action of individual
dephasing channels on cluster qubits is also studied. We show that the effect
of non-idealities is limited by using small clusters, which requires compact
schemes for computation. In light of this, we address an experimentally
realizable four-qubit linear cluster which simulates a controlled-{\sf NOT}
({\sf CNOT}).
