We demonstrate a wavelength-tunable, fiber-coupled source of polarization-entangled photons with extremely high spectral brightness and quality of entanglement. Using a 25 mm PPKTP crystal inside a polarization Sagnac interferometer we detect a spectral brightness of 273000 pairs/(s mW nm), a factor of 28 better than comparable previous sources while state tomography showed the two-photon state to have a tangle of T=0.987. This improvement was achieved by use of a long crystal, careful selection of focusing parameters and single-mode fiber coupling. We demonstrate that, due to the particular geometry of the setup, the signal and idler wavelengths can be tuned over a wide range without loss of entanglement.