From a formal viewpoint, the approach described herein constitutes a major extension, to product Hilbert spaces characteristic of open quantum systems, of our work on control- ling radiationless transitions in large molecules [12]. There, population transfer between a Q -subspace and the remainder of the Hilbert space, the P -subspace, was minimized by preparing initial superpositions in the Q -subspace, relying on the presence of overlapping resonances. This approach was applicable to the case where the full Hilbert space was par- titioned into the sum of two subspaces. By contrast, decoherence involves the effect of an environment on the system, i.e. a product of two Hilbert spaces. The difference is substantial and significant. The inter-relationship between overlapping resonances and the ability to design states that are resistant to decoherence is general. It proves useful, however, to introduce the approach via a specific generic example. For this reason we choose a particular class of spin- boson problems. Note that system decoherence is a manifestation of the loss of quantum information when one neglects the environment with which the system is entangled[4]. As such, decoherence can occur effectively even with a small environment[13] as is manifest in the example below. The structure of the paper is as follows. In Sec. II, we introduce a generic system that describes a spin system interacting with a environment, providing a specific example for this general approach. Section III, considers the nature of decoherence in this system, and its relationship to overlapping resonance. Some specific numerical examples are provided in Sect. IV to demonstrate correlations between overlapping resonances and reduced state decoherence. Sect. V provides a summary. The spin-boson problem has been extensively studied in Chemistry in various scenarios and for a wide variety of applications[14]. Here we consider, as a specific example, the control of decoherence in a simple spin system interacting with a small thermal environment, i.e. a single spin-half system and an environment comprising a single-mode oscillator. The most general system-environment Hamiltonian for this case is given by II. A GENERIC CLASS OF HAMILTONIANS H/ ℏ = ωa $^{†}$a + ω$_{0}$ 2 S$_{z}$ + g$_{r}$ ( S$_{+}$a + S$_{−}$a $^{†}$) + g$_{nr}$ ( S$_{+}$a † + S$_{−}$a ) + g$_{ph}$S$_{z}$ ( a + a $^{†}$) , (1) 3