We introduce an extended version of the dispersion-management (DM) model, which includes an extra nonlinear element, and consider transmission of return-to-zero pulses in this system (they are not solitons). The pulses feature self-compression, accompanied by generation of side peaks (in the temporal domain). An optimal transmission distance, z(opt), is identified, up to which the pulse continues to compress itself (the eventual width-compression factor is similar or equal to 2), while the amplitude of the side peaks remains small enough. The distance z(opt) virtually does not depend on the strength S of the DM part of the system in the interval 1.5 < S < 11, but it is sensitive to the nonlinearity strength in the extra segment. The system provides essentially stronger suppression of the noise-induced jitter of the pulses than the ordinary DM model. The most important issue is interaction between adjacent pulses, which is a basic difficulty in the case of DM solitons. In a broad parameter region, the system provides effective isolation between pulses. The minimum initial temporal distance between them, necessary for the isolation, is quite small, slightly larger than 1.5 the pulse's width. The transmission actually improves the quality of multi-pulse arrays, as it leads to deepening of hiatuses between originally overlapping pulses. (C) 2004 Elsevier B.V. All rights reserved.