The generation of the right amount of baryon asymmetry η of the Universe from supersymmetric leptogenesis is studied within the type-I seesaw framework with three heavy singlet Majorana neutrinos N_i (i = 1,2,3) and their superpartners. We assume the occurrence of four zeroes in the neutrino Yukawa coupling matrix Y_ν, taken to be μτ symmetric, in the weak basis where N_i (with real masses M_i > 0) and the charged leptons l_α (α = e,μ,τ) are mass diagonal. The quadrant of the single nontrivial phase, allowed in the corresponding light neutrino mass matrix m_ν, gets fixed and additional constraints ensue from the requirement of matching η with its observed value. Special attention is paid to flavor effects in the washout of the lepton asymmetry. We also comment on the role of small departures from high scale μτ symmetry due to RG evolution.