Silver nanowire (Ag NW) networks are promising candidates for replacement of indium tin oxide (ITO). However, transparent conductors based on Ag NW networks often suffer from 'haziness' resulting from surface roughness. Thus, in addition to achieving suitable transparency and conductivity, surface roughness must be minimized if realistic implementation of Ag NW networks as transparent conductors is to be realized. In this work, we have reduced the surface roughness of Ag NW networks to below 5 nm as compared to 54 nm for as-deposited Ag NWs through optimization of the low temperature annealing treatment and planarization by poly(3,4 ethylenedioxythiophene)-poly(styrenesulfanate). Using this method, we have been able to produce Ag NW networks with transmittances and sheet resistances of 87% and 11 Omega/sq, respectively. These are some of the best values reported for non-oxide-based transparent conductors. Incorporation of these smooth Ag networks into polymer light emitting diodes fabricated in our laboratory yields device characteristics that are comparable to or better than those with commercially available ITO.