No matter how tightly I shut the outside tap, it continues to run. What can I do?

Most garden spigots can be rebuilt. They come in many different types so can you take a picture of yours or find an example on the net, if so I can help you rebuild it. Google (http://www.google.com/#hl=en&sclient=psy-ab&q=outdoor+garden+spigots&oq=gaRDEN+SPIGOTS&gs_l=hp.1.2.0j0i5j0i5i30j0i8i30.1483.6358.0.9037.1 6.12.1.3.3.0.193.1963.0j12.12.0.les%3B..0.0...1c.e r41bffGkXo&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=ab1a020529bad5f7&biw=1239&bih=789)

Like Bob says the garden spigots comes in different typs, see the image below if your is one of them let us know, Thanks.

John