Acoustooptic tunable filters (AOTF) based on MC (matched cladding), DS (dispersion shifted) and DC (dispersion compensation) fiber were studied. It is found that the fiber with large waveguide dispersion is a promising candidate to reduce the bandwidth of AOTF. In order to describe the relations between the fiber dispersion and the filters bandwidth, a dispersion parameter N is defined and its relation to the tuning rate of the fiber AOTF is derived. This allows one to estimate the dispersion properties of a fiber by using the more easily measurable parameter of tuning rate. Experimentally, as narrow as 0.55 nm of FWHM bandwidth was demonstrated on commercially available DC fiber.