ggplot2: Determining the order in which lines are drawn

In a time series, I want to plot the values of an interesting cluster versus the background. However, if I'm not careful, ggplot will draw the items in an order determined by their name, so background items will obscure the interesting cluster:

Correct: Interesting lines in front of background

Wrong: Background lines obscure interesting lines

One way to solve this is to combine the label and name columns into one column that is used to group the individual lines. In this toy example, the line belonging to group 1 should overlay the other two lines: