We have measured shot noise in single-walled carbon nanotubes with good contacts at 4.2 K at low frequencies (f=600-850 MHz). We find a strong modulation of shot noise over the Fabry-Perot pattern; in terms of the differential Fano factor the variation ranges over 0.4-1.2. The shot noise variation, in combination with differential conductance, is analyzed using two (spin-degenerate) modes with different, energy-dependent transmission coefficients. Deviations from the predictions from Landauer-Buttiker formalism are assigned to electron-electron interactions.