Coagulation values (CVs) of cellulose/1-ethyl-3-methylimidazolium acetate (EmimAc)/dimethyl-sulfoxide (DMSO) solutions for water, ethanol (EtOH) and 2-propanol (2-PrOH) were measured by using a light-scattering technique. Expressed in moles per mole, CVs of H2O were roughly twice as high as the CVs of EtOH and 2-PrOH at equal cellulose concentration for EmimAc solutions without the addition of a cosolvent. We explain this observation mainly in terms of alcohol alkyl chains efficiently obstructing EmimAc anions, preventing anions from simultaneously interacting with cellulose hydroxyls. DMSO was found to mitigate the coagulating effect of water and, to a lesser extent, the effect of alcohols. The explanation may be the different enthalpies of mixing for water and alcohols, with DMSO. An explanation on a more practical level, is based on how the solvatochromic α and β parameters change due to small amounts of the different non-solvents. Small additions of methanol induce disproportionately large changes from basic towards acidic properties for DMSO, meanwhile, the same stoichiometric addition of water induces only minor changes. Precipitation occurred at concentrations of non-solvent much higher than the concentrations that limit dissolution. The most likely explanation for this is a metastable region in the phase diagram. It was also seen that the typically observed inhibitive effect of high Mw on solubility during dissolution did not apply to precipitation.