The highland region of Ishtar Terra on Venus has mountains that reach up to 11 km in height and are thought to be basaltic in composition. Assuming that dynamic uplift of crust to this height is unlikely, we examine the topography produced by an isostatically supported thickening basaltic crust. It is found that regardless of whether the crust thickens by crustal shortening or by volcanic construction, the high-density basalt-eclogite phase transition is the limiting factor for producing significant elevation of the mountains. The maximum height attained by basaltic mountains depends on the nature of the basalt-eclogite phase transition. Without a phase transition, a basaltic crust must thicken to greater than 100 km to reach heights over 10 km. An instantaneous phase transition of basalt to eclogite allows a maximum topographic height of less than about 2 km. However, with a time lag of 100 Ma owing to slow rates of solid-state diffusion, our calculations show that the mountains can reach elevations greater than 10 km only if they are less than 25 Ma old. Higher temperatures within the Venusian crust may decrease the extent of the stability fields of high-density basalt phases and allow high topography if the thickening crust melts. This can occur if the radioactive element concentrations measured on the surface of Venus are uniformly distributed throughout the crust, the crust thickens to greater than 65 km, and the thickened crust is older than about 400 Ma. The conflicting results of a young age predicted for high basaltic mountains and an almost uniform surface age of 500 Ma from crater populations, coupled with similarities in bulk physical properties of Venus and Earth, suggest that the basaltic surface composition found at several landing sites on the planet may not be representative of the entire crust. We suggest that Ishtar Terra formed from the collision of continent-like highly silicic cratons over a region of mantle downwelling. Lakshmi Planum resulted from the thickening of a basaltic crust and the peripheral mountain belts formed from the collision of granitic cratons that were pulled toward a downwelling region of mantle.