Optical filters tunable for both center wavelength and bandwidth, having applications such as in astronomy, remote sensing, laser spectroscopy, and other laser-based sensing applications, using Michelson interferometers or Mach-Zehnder interferometers modified with Gires-Tournois interferometers ("GTIs") are disclosed. A GTI nominally has unity magnitude reflectance as a function of wavelength and has a phase response based on its resonator characteristics. Replacing the end mirrors of a Michelson interferometer or the fold mirrors of a Mach-Zehnder interferometer with GTIs results in both high visibility throughput as well as the ability to tune the phase response characteristics to change the width of the bandpass/notch filters. A range of bandpass/bandreject optical filter modes, including a Fabry-Perot ("FP") mode, a wideband, low-ripple FP mode, a narrowband notch/bandpass mode, and a wideband notch/bandpass mode, are all tunable and wavelength addressable.