In this work we discuss different factors governing coil-globule coexistence in the compaction process of DNA. We initially analyse the role played by fluctuations in the degree of binding of an external compacting agent in the conformational behavior of the chain backbone. The analysis relies both on Monte Carlo simulation results and simple statistical approaches. Compacting agents of various binding characteristics are taken into consideration and the degree of charge neutralization upon the chain is related to conformational indicators. Selected model systems comprising stiff chains in the presence of multivalent ions are employed to assess intrinsic single-chain conformational fluctuation, in the presence of external agents but not resulting from differences in binding. It is shown that trends found for a variety of compacting agents, including the extension of the coil-globule coexistence regions, can be rationalised on the basis of this analysis.