In two-dimensional homonuclear experiments, reliable detection of very small cross peaks is sometimes hampered by t1-noise from larger diagonal peaks which have the same F2 frequency. This t1-noise can be selectively removed by recording partial 2D spectra using the double pulsed field gradient spin echo (DPFGSE). Resonances not selected by the DPFGSE do not contribute any t1-noise to the resulting spectrum. The absence of t1-noise from the diagonal peaks render the small cross peaks at the same F2 frequency observable. The success of this technique is shown by partial 2D NOESY and TOCSY spectra.