  An edge-colored graph $G$ is called properly colored if no two adjacent edges
share a color in $G$. An edge-colored connected graph $G$ is called properly
connected if between every pair of distinct vertices, there exists a path that
is properly colored. In this paper, we discuss how to make a connected graph
properly connected efficiently. More precisely, we consider the problem to
convert a given monochromatic graph into properly connected by recoloring $p$
edges with $q$ colors so that $p+q$ is as small as possible. We discuss how
this can be done efficiently for some restricted graphs, such as trees,
complete bipartite graphs and graphs with independence number $2$.
