The first step is to identify the plant. Purple loosestrife (Lythrum salicaria) and several related species look much alike, and all are quite invasive. Some good photographs are posted on The Nature Conservancy Invasive Species Initiative website at http://tncweeds.ucdavis.edu/esadocs/lythsali.html. Introduced from Europe in the early 1800s, purple loosestrife is now the target of 21 states struggling to keep it out of natural wetlands, where it often forms dense colonies and chokes out native plants. All of the states in the upper Midwest restrict the use of purple loosestrife in gardens, because just one healthy plant can produce 2.5 million seeds. If you identify your plant as purple loosestrife, dig it out and destroy it. In addition to a stout taproot, expect to find a network of shallow roots spreading from the primary plant. If the plant in your garden is holding seeds, place a paper or plastic bag completely over the seed-bearing spikes and clip them off before you begin digging, to prevent accidentally spreading seeds.