We produced 5-mJ, 6.5-fs visible pulses at a repetition rate of 1 kHz using filamentation in a gas cell filled with kryptonfollowed by spectral selection and phase compensation by a combination of dielectric mirrors. The visible pulses have a smooth spectrum from 520 to 650 nm with a shot-to-shot stability in each spectral component of better than 2% (standard deviation). This pulse compression scheme is simple and robust, and can be easily integrated into intense ultrashort-pulse laser systems.Program for Leading Graduate Schools (MERIT) by Japan Society for the Promotion of Science.