An innerduct for a cable containing one or more strip-shaped lengths of woven textile fabric configured to create a flexible, longitudinal compartment for enveloping a cable. The woven fabric comprises a plurality warp yarns and a plurality of picks of weft yarns, the weft yarns contain a repeating first weft pattern of at least one monofilament yarn and optionally at least one single-inserted multifilament yarn. The woven fabric contains an alternating pattern containing first weave zones and partial float weave zones. The warp yarns in the first weave zone pass successively over and under each adjacent weft yarn and at least a portion of the warp yarns in the partial float zone float over some adjacent weft yarns.