Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal coding allows to achieve DC control, in addition to satisfying the runlength limited (RLL) constraint specified by the recording channel. In this work, a study is initiated on bi-modal fixed-length constrained encoders. Necessary and sufficient conditions are presented for the existence of such encoders for a given constraint. It is also shown that under somewhat stronger conditions, one can guarantee a bi-modal encoder with finite decoding delay.