The manipulation and processing of single-wall carbon nanotubes (SWNTs) is limited by their poor solubility in most common solvents. Covalent sidewall functionalization of SWNTs provides an excellent route to improve their solubility. Here we have studied the relationship between sidewall functionalization and phase behavior of solutions of functionalized SWNTs (f-SWNTs) in strong acids. We use centrifugation in conjunction with UV-Vis-nlR spectroscopy to quantify the solubility of f-SWNTs in strong acids. We image the dispersions of functionalized tubes by polarized light microscopy. We find that adding butyl groups increases marginally the solubility of SWNTs in 102% sulfuric acid in the isotropic phase; adding 9-nonadecyne groups roughly doubles the solubility of SWNTs. Viscosity measurements in dilute solutions are sensitive to de-bundling. We compare the viscosity-concentration dependence of dilute pristine and f-SWNTs to assess whether and how functionalization promotes de-bundling and stabilizes the tubes. The phase behavior and rheology of these f-SWNTs parallels with that of pristine SWNTs; 9-nonadecylated SWNTs have higher solubility and should be easier to process.