RLL modulations that have d equals 1 constraint, such as RLL(1,7) 1) ,2), are widely used in the optical disk systems to enlarge a window margin. While 2 to 3 variable length modulations, which is representative coding rate for those modulations, were difficult to control digital sum variation (DSV), a common solution is inserting marginal bits2). However a drawback of this method is a loss on the recording capacity. This paper introduces new RLL(1,k,4,6) modulations which can generate various k constraint, k equals 7 or above, codes with a cording table. All of those have 4 to 6 fixed coding rates and can control the DSV without marginal bits. It can be emphasized that all the modulations use the same coding table and the same decoder. The table is constructed by 4 states sliding block encoder. Since code words by the (1,k,4,6) modulation is decoded only by a symbol look-ahead decoder, error propagation is within 8 data bits. The high coding rate and sufficient DSV control ability can bring an extra capacity or system margin.