We provide a very simple adaptation of our recently published quantum Monte Carlo algorithm in full configuration-interaction (Slater determinant) spaces which dramatically reduces the number of walkers required to achieve convergence. A survival criterion is imposed for newly spawned walkers. We define a set of initiator determinants such that progeny of walkers spawned from such determinants onto unoccupied determinants are able to survive, while the progeny of walkers not in this set can survive only if they are spawned onto determinants which are already occupied. The set of initiators is originally defined to be all determinants constructable from a subset of orbitals, in analogy with complete-active spaces. This set is dynamically updated so that if a noninitiator determinant reaches an occupation larger than a preset limit, it becomes an initiator. The new algorithm allows sign-coherent sampling of the FCI space to be achieved with relatively few walkers. Using the N(2) molecule as an illustration, we show that rather small initiator spaces and numbers of walkers can converge with submilliHartree accuracy to the known full configuration-interaction (FCI) energy (in the cc-pVDZ basis), in both the equilibrium geometry and the multiconfigurational stretched case. We use the same method to compute the energy with cc-pVTZ and cc-pVQZ basis sets, the latter having an FCI space of over 10(15) with very modest computational resources.