We examine the Martian valley networks in the framework of topographic influences on precipitation. We use an analytical model and the Laboratoire de Météorologie Dynamique (LMD) early Mars global circulation model (GCM) to explore the local-scale distribution of orographically forced precipitation as a function of atmospheric pressure. In simulations with 500 mbar and 1 bar CO2 atmospheres, orographic lifting results in enhanced snowfall upslope of the observed valley network tributaries. Our framework also suggests that a 2 bar atmosphere cannot create the observed valley pattern at the highest-relief valley network, Warrego Valles. As in previous work, the GCM does not generate temperatures warm enough for rain or significant snowmelt in the highlands with CO2 greenhouse warming alone. Thus while transient periods of unusual warming are still required to melt the deposits and carve the valleys, our model predicts snow deposition in the correct locations.