Recent studies have shown that the prospects for significantly increasing bunch intensities in the LHC for the luminosity upgrade (HL-LHC) may be severely limited by the available cryogenic cooling capacity and the electron-cloud (EC) driven beam instability. However, it is planned that during the HL-LHC era the bunch intensities in the LHC will go up by nearly a factor of two compared to the LHC-design values. This motivates the exploration of additional EC mitigation techniques that can be adopted in addition to those already in place. Preliminary simulations indicated that long flat bunches can be beneficial over Gaussian bunches to reduce the EC build up. Rigorous studies using realistic bunch profiles have never been done. Therefore, we have undertaken an in-depth investigation in the CERN 26 GeV PS to see if we can validate the previous findings and, in particular, if flattening the bunch can mitigate the EC. Here we present the results from dedicated EC measurements in the PS using a variety of bunch shapes and a comparison with simulations. Finally, we investigate if reshaping the bunch profiles using a 2nd harmonic rf cavity can mitigate EC in the HL-LHC.