  An "edge guard set" of a plane graph $G$ is a subset $\Gamma$ of edges of $G$
such that each face of $G$ is incident to an endpoint of an edge in $\Gamma$.
Such a set is said to guard $G$. We improve the known upper bounds on the
number of edges required to guard any $n$-vertex embedded planar graph $G$:
  1- We present a simple inductive proof for a theorem of Everett and
Rivera-Campo (1997) that $G$ can be guarded with at most $ \frac{2n}{5}$ edges,
then extend this approach with a deeper analysis to yield an improved bound of
$\frac{3n}{8}$ edges for any plane graph.
  2- We prove that there exists an edge guard set of $G$ with at most
$\frac{n}{3}+\frac{\alpha}{9}$ edges, where $\alpha$ is the number of
quadrilateral faces in $G$. This improves the previous bound of $\frac{n}{3} +
\alpha$ by Bose, Kirkpatrick, and Li (2003). Moreover, if there is no short
path between any two quadrilateral faces in $G$, we show that $\frac{n}{3}$
edges suffice, removing the dependence on $\alpha$.
