q3dfit performs PSF decomposition and spectral analysis for high dynamic range JWST IFU observations, allowing the user to create science-ready maps of relevant spectral features. The software takes advantage of the spectral differences between quasars and their host galaxies for maximal-contrast subtraction of the quasar point-spread function (PSF) to reveal and characterize the faint extended emission of the host galaxy. Host galaxy emission is carefully fit with a combination of stellar continuum, emission and absorption of dust and ices, and ionic and molecular emission lines.