Motivated by STIS observations of more than 50 nearby galactic nuclei, we consider long-slit emission-line spectra when the slit is wider than the instrumental PSF, and the target has arbitrarily large velocity gradients. The finite width of the slit generates complex patterns in the spectra that can be misinterpreted as coming from various physically distinct nuclear components, but when interpreted correctly, they can have considerable diagnostic power. For a thin disk in circular motion around a central galactic black hole (BH), a characteristic artifact occurs in the spectrum at the outer edge of the BH's sphere of influence. It betrays the presence of a BH, and allows us to develop a new method for estimating its mass, which gives higher sensitivity to BH detection than traditional methods.