Often, you find yourself using the Trim command to tidy up loose ends of lines. If this is the case, don't bother selecting cutting edges, just use the "select all" option.
Start the Trim command, ModifyTrim from the pull-down menu or TRIM from the command line. At the prompt, simply hit (Enter) to accept the <select all> option.
Now, just pick the line ends you want to remove.
There's another old trick. We hardly ever use CHAMFER, so we use it to clean-up corners. Set the distance of the chamfer to "0", select the two lines...and you have two lines that meet with no overlap.