We consider insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. We further assume that there are no segment markers in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of VT codes chosen with pre-determined prefixes and/or suffixes. The proposed codes are zero-error, can be decoded segment-by-segment, and their rate scaling as the segment length increases is the same as that of the maximal code.