Definition: A graph is k-edge-choosable if whenever we assign a list of k colors to each edge, it is possible to choose one color for each edge from its list, so that incident edges receive different colors. This is a generalization of k-edge-colorability.
Abstract: We show that if G is a planar graph with no two 3-faces (regions bounded by 3-cycles) sharing an edge and with maximum degree Delta(G) not equal to 5, then G is (Delta(G)+1)-edge-choosable. This improves results of Wang and Lih and of Zhang and Wu. We also show that if G is a planar graph with Delta(G)=5 and G has no 4-cycles, then G is 6-edge-choosable. In addition, we prove that if G is a planar graph with Delta(G)=5 and the distance between any two 3-faces in G is at least 2, then G is 6-edge-choosable. Finally, we prove that if G is a planar graph with no two 3-faces sharing an edge and with maximum degree Delta(G) at least 7, then G has an edge uv with degree sum d(u)+d(v)at most Delta(G)+2. All of our results use the discharging method.