In this paper, we propose a new relaxation of the single-peaked property by constraining the net preference matrix instead of the preference profile. More precisely, this new domain restriction holds for a given profile P if there exists a single-peaked profile P' with the same net preference matrix as P. We provide a characterization of net preference matrices that can be “implemented” by a single-peaked profile, and propose a polynomial time algorithm to recognize these matrices. In cases where preferences are not net single-peaked, we recall a dynamic programming approach for obtaining an axis over candidates such that the net preference matrix respects as much as possible (in some sense) our net single-peakedness condition. We also formulate an integer linear program for partial net single-peakedness. Finally we present the results of numerical tests on real election data.