In this work we address the problem of speeding up navigational queries over compact planar graphs. In particular, we work over one of the most practical representations for compact planar graphs, which is based on the decomposition of the graph into one arbitrary spanning tree and a second one induced by the former. We propose a new optimization model that captures the desired topological properties of the first spanning tree. For this model, we propose several heuristics, which we experimentally compare on our application domain. The experimental results support that the model indeed captures the main properties that allow us speeding up the main navigational queries over several benchmarks.